Idioms are common expressions that have a figurative meaning. You need to understand them in a creative manner, and not in a literal manner. Phrasal verbs use a common verb plus a preposition or adverb to create a new meaning. This is common English. The trick is to look at the phrasal verb in context, and not as a set definition. An expression simply means the way something is said or written. This usually a non-literal meaning, so I agree with Naga's explanation.

Please note that in American English, "caught short" does not mean an urgent need to use the bathroom. That is a UK and Australian usage. In the USA, it means to be unprepared for something or to temporarily run out of cash.

An idiom and an expression could be the same: for instance, 'To be caught short' means to have an urgent need for the bathroom. You could say that this is an idiom but you could also call it an expression. Idioms are often metaphorical too; such as 'hoist on one's own petard', which means to injure oneself using the means by which one intends to injure others. A phrasal verb is simply a verb with more than one word in it: 'To fall off' of instance or 'to blow up'.