Speed, rate, pace, tempo: what's the difference?

I looked up these three words in Oxford Dictionary and I found that they seem to be interchangeable in some cases.

Here's the question: what's the difference between the three words?

Rate: [countable] a measurement of the speed at which something happens.

Most people walk at an average rate of 5 kilometres an hour. At the rate you work, you'll never finish!

Pace: [singular, uncountable] the speed at which something happens.

It is difficult to keep up with the rapid pace of change. We encourage all students to work at their own pace (= as fast or as slow as they can).

Speed: 1 [countable, uncountable] the rate at which somebody/something moves or travels.

He reduced speed and turned sharp left.

Speed 2 [countable, uncountable] the rate at which something happens or is done.

This course is designed so that students can progress at their own speed.

Speed: 3. [uncountable] the quality of being quick or rapid

The train began to pick up speed (= go faster). Increasing your walking speed will help to exercise your heart.

The accident was due to excessive speed. Speed is his greatest asset as a tennis player.

Tempo: the speed of any movement or activity

the increasing tempo of life in Western society

Don’t let the other team dictate the tempo of the game

• Very roughly, "speed" is the distance traveled per unit time, while "pace" is the number of operations (which may be, eg, footsteps) that occur per unit time. "Rate" is kind of like speed, only measuring some other quantity (eg, liters volume) per unit time. But all three tend to be used very loosely and often interchangeably, and each may be used with different (and likely more precise) definitions in certain industries or occupations. Nov 1, 2015 at 2:27
• Be aware that rate is also used to indicate prevalence in a population. This is a misnomer but well established. When you see that the annual murder rate someplace is 19.2, you might be tempted to think that means an average of 19.2 people are killed there each year, but it really means that for every 100,000 residents, 19.2 are homicide victims. Nov 1, 2015 at 3:48
• @deadrat thanks, but now I'm completely baffled by the fact that the murder rate of the town I used to live in was 1 in 7 years and it was considered high for the area. Nov 1, 2015 at 3:54
• @MattSamuel The murder rate is usually stated for a year. So let's say your town has 5,000 people. For the year in which the murder occurred, your town's murder rate is 20 per 100,000. In 2014, the murder rate in Chicago was 14.8, but there are a lot more people in Chicago, about 2.7M, so there were a lot more homicides in Chicago, but the "rate" was lower because your town is so small. Nov 1, 2015 at 4:21

Those 4 words above-mentioned are sometimes used interchangeably, but there are some clear distinctions.

Pace originally meant:

late 13c., "a step in walking; rate of motion," from Old French pas "a step, pace, trace," and directly from Latin passus, passum "a step, pace, stride," noun use of past participle of pandere "to stretch (the leg), spread out,"

[Online Etymology Dictionary]

Therefore, you use "pace" in place of speed to describe something slow and steady.

For example, you use a "pace-maker" in stead of "speed-maker" for your heart device or someone who sets the pace in a race such as marathon as it means:

A person or animal who sets the pace at the beginning of a race, sometimes in order to help a runner break a record

A device for stimulating the heart muscle and regulating its contractions.

[Oxford Online Dictionary]

However, if you describe a car or an airplane, you don't use "pace" for its "speed".

Tempo originally meant:

"relative speed of a piece of music," 1724, from Italian tempo, literally "time" (plural tempi), from Latin tempus "time, season, portion of time" (see temporal). Extended (non-musical) senses by 1898.

[Online Etymology Dictionary]

You also use "tempo" in place of speed to describe something slow and steady as it means:

The speed at which a passage of music is or should be played. The rate or speed of motion or activity; pace:

[Oxford Online Dictionary]

Rate originally meant:

"estimated value or worth," early 15c., from Old French rate "price, value" and directly from Medieval Latin rata (pars) "fixed (amount)," from Latin rata "fixed, settled," fem. past participle of reri "to reckon, think" (see reason (n.)). Meaning "degree of speed" (properly ratio between distance and time) is attested from 1650s. Currency exchange sense first recorded 1727. First-rate, second-rate, etc. are 1640s, from British Navy division of ships into six classes based on size and strength. Phrase at any rate originally (1610s) meant "at any cost;" weakened sense of "at least" is attested by 1760.

[Online Etymology Dictionary]

Rate is often used for "frequency" or "quantity".

‘the island has the lowest crime rate in the world’
‘buying up sites at a rate of one a month’

It can also mean:

"The amount of a charge or payment expressed as a percentage of another amount, or as a basis of calculation: ‘you’ll find our current interest rate very competitive’

(rates) (In the UK) a tax on commercial land and buildings paid to a local authority; (in Northern Ireland and formerly in the UK) a tax levied on private property.

[Oxford Online Dictionary]

You use "economic growth rate" not "economic growth speed" when it is expressed in a percentage.

Conclusion: The etymological roots of those four words can shed more light on their different usages.

Speed commonly refers to the constant rate of change over a distance. That is, it is commonly associated with movement across a distance. It is notated as the distance over time as in km/hr.

Rate is a description of change over time. It doesn't have to do with distance (as with speed). For example, the flow rate is the rate at which a liquid flows through a medium. It is used to indicate that the preceding is a measurement of work. Other examples are descent rate, heart rate (which is actually the heartbeat), etc.

Pace describes the rate of change; and like speed it can also describe a change in distance. However, unlike speed - pace is measured as time over distance; for example: 3 minutes / mile.

In addition, pace is often used to describe the relative rate of work/action. For example; "He is walking at a fast pace." or "They couldn't keep up with the pace of work".

Tempo is specifically the rate at which a music piece must be played. It is the only one of the four that is tied to a specific area or practice (pace, rate and speed are generic).

Tempo is measured in beats per minute; and specific rates are given their own description - mostly from Italian. For example, Presto means bpm between 168 and 200. Wikipedia has a nice list of these.

In modern vernacular - tempo has been used interchangeably with pace; especially when associated with non-music related events. For example, "They opposition upped the tempo of the game".