I think I have a notion what is what but maybe you know a good definition what is what? For example "Hindsight is always 20:20" — is that a proverb or an idiom?
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An idiom is an expression that can be understood only as a whole and not by analysing its constituent parts. For example, if you know what ‘kick’, 'the’ and ‘bucket’ mean, that won’t help you understand that ‘kick the bucket’ means ‘die’. A proverb may or may not be idiomatic, but it expresses succinctly some form of philosophy, folk wisdom or advice. 'Hindsight is always 20:20' is neither an idiom nor a proverb, but a trite expression of the obvious.
Idioms are short arrangements of words that have a meaning beyond their literal. They can be completely different from their literal meaning, such as "bite the bullet", or "step up to the plate", both of which mean "begin a difficult task." Or they can mean close to their literal meaning, but carry lots of cultural baggage along with them, such as "land of the free" which means what it says, but carries lots of American patriotic baggage, or "tea and sympathy" which denotes a rendezvous with a particular goal of commiseration in mind.
A proverb is, instead, a short or pithy remark or story designed to convey a moral or practical message. It comes from the eponymous book of the Bible which, in many chapters, has pages and pages of one or two verse statements of that kind. "Better to meet a bear robbed of her cubs than a fool in his folly", "A fool and his money are soon parted." etc.
Proverbs are usually pretty literal in their meaning, and are certainly not restricted to those from the Bible, though that is the origin of the name and the form as used in English. Some non-Biblical proverbs would be "many hands make light work", "procrastination is the thief of time", etc.
A proverb is usually a sentence that evokes a sense of wisdom. While most of the time it can refer to a certain sense of wisdom, proverbs are mere expressions of truth based on common sense or practicality.
Ex Once bitten, twice shy.
When the cat is away, the mouse will play.
An idiom is a string of words that when taken together has a meaning different to its literal interpretation. The meaning should be taken figuratively.
To keep one's head above the water= to manage a situation
Firstly, it must be recognised that the term 'idiom' is highly polysemic and has been given different conflicting senses by various linguists. In fact, Strassler's 1982 Idioms in English. A Pragmatic Analysis. spends pages covering this, and includes the worrying
According to [M H Roberts'] definition, there is no element in [any] language that is not either an idiom or the constituent of an idiom.
But I agree with Strassler that perhaps the best definition of an idiom is that given in the OED and Supplement to the OED (see previous link) sense 3a:
A form of expression, grammatical construction, phrase etc peculiar to a language; a peculiarity of phraseology approved by the usage of a language, and often having a significance other than its grammatical or logical one.
More simply, an accepted expression using non-standard or at least very unusual grammar and/or word-sense, and having a meaning beyond the obvious.
Consider the well-known adage
Where there's smoke, there's fire.
Is it an idiom?
It doesn't contain any extragrammatical construction, and the statement can be taken at face value (even though it's usually used metaphorically – see below). One could argue that using fire to represent something dire not immediately apparent (imagine a fire miles away in a forest or hidden behind tall buildings), and smoke a secondary indicator (eg rumour, police interest) fulfils the 'using words in a peculiar way' requirement for an idiom.
But I'd be more precise and say that 'Where there's smoke, there's fire' is not an idiom, but uses the extended metaphor
fire (the 'tenor') = (represents) something bad (the vehicle), often wicked (cf Prov 26:20, NAS: For lack of wood the fire goes out, And where there is no whisperer, contention quiets down)
and smoke (a second but related tenor) = rumour or acknowledged general discussion (but note that fire usually represents other things in the Bible).
As stated above, 'Where there's smoke, there's fire' actually makes sense literally (though admittedly sounds old-fashioned nowadays); it's the intended metaphorical usage that gives the words 'smoke' and 'fire' new 'meanings' (or rather implications). So I'd not call this an idiom, though I wouldn't argue too strongly with those who do. It's something of a grey area.
A metaphor is a device where one situation etc is expressed graphically in terms of another concept (with obvious needs not to stretch the analogy too far).
- A figure of speech in which a word or phrase that ordinarily designates one thing is used to designate another, thus making an implicit comparison, as in "a sea of troubles" or "All the world's a stage" (Shakespeare).
He's a tiger means he's a fierce opponent, especially when cornered, but doesn't mean he's got a long striped tail.
There are well-known more general metaphors, often ontological:
ontological (eg container) metaphor
Examples: The following sentences express the activity-as-container metaphor:
How did Jerry get out of washing the windows?
Outside of washing the windows, what else did you do?
How did you get into window-washing as a profession?
I put a lot of energy into washing the windows.
I get a lot of satisfaction out of washing windows.
He's on the up and up (the 'becoming increasingly successful' sense) makes use of the pervasive up-is-good/health/to be desired/success metaphor.
A proverb is a widely used concise statement of a generally acknowledged truth, whether using a literal or metaphorical approach. So 'There's no smoke without fire' is obviously a proverb.
- A short pithy saying in frequent and widespread use that expresses a basic truth or practical precept.
With OP's example "Hindsight is always 20:20"
we have an obviously fixed expression expressing a widely acknowledged truth (admittedly using hyperbole), and I'd say it's in common enough use to qualify as a proverb. Metaphor is involved (only physical sight is measurable from a standard 20 foot distance). As for idiom status, even though 20:20 could be said to be being used in an offbeat way here, that's only because of the intended metaphor (and a tendency towards with-it vocabulary), so I would not say an idiom is involved here (others might disagree).