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Idioms are groups of words having figurative meaning. It is generally not the literal meaning of the words and difficult to get the exact message until the context of those words is followed.
For e.g.
A chip on your shoulder - means you are holding a grudge

Phrases are the words that may not necessarily have figurative meaning.It generally expresses a concept and is used as a single unit within a sentence
For e.g.
The lost puppy was a wet and stinky dog.
In this sentence (lost puppy and wet stinky dog are phrases)