Adage
A proverb or short phrase that expresses a generally accepted truth.
Example: A picture paints a thousand words
Aphorism
Similar to an adage, but with a terse or pithy edge, possibly unwelcome to the listener.
Example: Blood is thicker than water
Euphemism
Expressions that, by using coy coded language, avoid direct references to potentially embarrassing topics. Often used to avoid referring to socially awkward matters like sex, death, war or defecation.
Example: All the way
Proverb
A proverb is a brief, simple expression, often giving advice or conveying an accepted truth based on the beliefs and experience of the culture it was created in. Many proverbs were coined in mediaeval England and consequently refer to antiquated topics.
Example: Don’t look a gift horse in the mouth
Slang
Slang is a form of language rather than a type of expression but there are so many slang phrases it is worth including here. Slang is characterised by its informality and frequent use of words that are most familiar to sub-groups within society – for instance, to criminals ‘bird’ = jail time, to the young ‘dench’ = cool and to golfers a ‘beach’ = a sand bunker. And, of course, Londoners have a long list of Cockney rhyming slang expressions.
You need to be careful when using slang phrases and know that the audience you are addressing is likely to understand them and also not be offended by them. Much slang refers to sex, sometimes very crudely so.
Example: Photo bomb