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I'm not asking about them as adjectives, or the calculus definition of 'differential'. ODO doesn't distinguish them, and synonymizes 'differential' with 'difference'.

In 1, can 'differences' substitute 'differentials? What'd change?

Source: The European Union: A Beginner's Guide. p. 139 Bottom - p. 140 Top. I, and not the book, bolded.

Gender has traditionally played a key role in the pricing of insurance policies.
  In 2004 an EU Directive prohibited all discrimination based on sex in the access to a supply of goods or services. In principle the Directive therefore prohibited the use of gender as a method of determining insurance premiums and benefits with regard to contracts that were entered into after 21 December 2007. However, the Directive also stated differential pricing could be maintained where statistical evidence supported such an approach. Insurance companies regarded this as crucial because as women drivers are statistically proven to have fewer accidents than male drivers, premiums for female insurance policies have generally been lower. In a similar way, because women live longer, men have traditionally received a higher rate from their pension annuities because their life expectancy is lower and as such their pension savings are able to produce more income over a shorter time.
  Such continued practice of price [1.] differentials was subject to a review after the Belgian Constitutional Court asked the European Court of Justice to assess the validity of differential pricing. This in turn resulted in the ECJ ruling on 1 March 2011 that insurers cannot charge different premiums to men and women based on their gender from 21 December 2012 onwards. In the case of car insurance, the significance of this ruling is that female car insurance premiums will rise while male insurance premiums will fall. And where high costs of insurance have in the past discouraged young men from buying fast cars that are more likely to lead to road accidents, a reduction in insurance costs could worryingly result in greater purchases of high performance cars.

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    What is the difference between this question and the questions in tchrist's comment? – Lawrence Jan 17 '18 at 8:04
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    I'm confused. This question looks like a complete duplicate of 'different' vs 'differential' (adjectives) The text u exactly the same, the words "differential" and "difference" are the same. The only difference I can tell is that here the OP mentions nouns whereas the term adjectives is used in the older question. – Mari-Lou A Jun 8 at 15:37
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    And it's the same question asked four years ago in ELL different vs differential (adjectives, not nouns) This should be mentioned in the present post and explained why none of the three answers posted on ELL satisfied the OP. – Mari-Lou A Jun 8 at 15:42
  • @Mari-LouA This question has become slightly perverse. differential pricing=difference in pricing, precisely a noun vs. adjective thang. The last question on ELL was also about an economics text that said that. Unfortunately, one has to explain the difference adjectivally. Ha ha. – Lambie Jun 10 at 13:24
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The two have significantly different expectations with regard to the structure of what is being compared, and differential is much more restrictive.

Taking the insurance actuarial table as an example — suppose the insurance rate is determined by looking a number up in a table. There are three indices — age, sex, and geographical location. So you can talk about the rate differential between genders because the gender subtables both have a parallel data structure. You can make the comparison element by element.

Using differential implies that you know the data structures are the same, and that you are restricting your comparisons to an element by element comparison across the common indices.

It does not make sense to use differential when making a "black box" comparison. For instance, unless you know the rate table has an index for marital status, you can't talk about the differentials between married and unmarried rates. These can only be described as differences, and would normally be some statistical values such as averages over large samples of customers.

Looking at this sentence —

However, the Directive also stated differential pricing could be maintained where statistical evidence supported such an approach.

This works only if the tables for men an women share the exact same indices. If the table for men had age and location as indices, and the table for women had marital status and educational level as indices, the statement wouldn't make sense. You would talk of rate differences, not rate differentials.

So I understand the above sentence to mean that using different indices to actuarialize the rates of men and women would be considered discriminatory, using the same indices, but assigning different rates to the elements would be conditionally allowed.

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    Does actuarial have a verb form? differential prices=difference in prices. Ain't no doubt about it. rate differences can be expressed as: differential rates. Just can't get that pesky adjective off our back. – Lambie Jun 10 at 13:27
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They're very, very similar.

Your specific question is whether

Such continued practice of price differentials was subject to a review after the Belgian Constitutional Court asked the European Court of Justice to assess the validity of differential pricing.

and

Such continued practice of price differences was subject to a review after the Belgian Constitutional Court asked the European Court of Justice to assess the validity of differential pricing.

are (a) both good English and (b) exactly equivalent. The answer to (a) is, yes, both are fine. The answer to (b) is a little longer winded.

They're both ultimately noun forms of the Latin verb differre, originally meaning carry/bear/remove in two directions. Difference is more or less exactly the deverbal differentia: a thing/amount/quality/&c. that separates two things or the state of being separated itself. Differential is a substantive formed in English from our version of differentia’s adjectival form differentialis. It mostly covers the same ground but isn’t used for the state of separation itself. That’s not what you’re talking about here, so the ODO is telling you they’re interchangeable.

The short version of why they ‘feel’ different to native speakers is that difference is more straightforward, common, and general. The only reasons to have differential at all is to sound a little smarter or to put a little more exactness on the kind of difference intended. Per its OED entry, that began with medieval logicians using it for 'specific distinguishing differences'; followed by natural philosophers using it for 'infinitesimal notional differences' in their groping towards calculus; followed by machinists using it for 'gears permitting different rates of rotation in wheels powered by the same motor' and botanists using it for 'specific distinguishing differences' again and economists using it as a smarter term for 'monetary differences in the prices/fees/wages/&c. between the categories/scenarios/&c. under discussion.'

So to summarize: some specialist fields will have precise ideas about ‘differential’ that don’t apply to ‘difference;’ from its application to math and gears, it often picks up a connotation of differing by increments; but it can a pretentious synonym for ‘different’ most of the time too.

The distinction between ‘different pricing’ and ‘differential pricing’ is that the latter is going to feel like it’s specifically talking about price differences between fixed categories of markets/customers/goods/&c. It doesn’t have to mean precisely that, but if you didn’t intend that more exact sense it would be clearer to just say ‘different’ in the first place.

In your precise example, ‘price difference’ does work as a rather exact synonym because you’ve already established the context that the differences under discussion are between genders. That won’t always be the case elsewhere, since it won’t always convey the nuance that ‘differential’ has in certain fields.

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"differential" immediately brings its mathematical use to my mind, where we put slightly increasing values in the variable of a function and see how the value of the function changes. The key word is "variable". Difference is more of a fixed value between two entities. In both 1 and 2, the pricing is done 'variably' according to the several factors (which would mathematically determine the value of the function). In 3, the difference is more pronounced, that is, difference in the pricing of premium for men and women. I hope this clarifies the difference!

  • @Greek-Area51Proposal - I think you did not pretermit them. In fact you explicitly disallowed them. – Jim Jun 9 at 6:43
  • @Jim Thanks. You're correct! I'm uncertain why I typed 'pretermit'. I explicitly ruled out the mathematical definition in my title and post. – Greek - Area 51 Proposal Jun 9 at 19:09

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