None - they mean the same thing.
The two are the same and are used interchangeably.
"Idom" is not a word in English, so the difference is between a word and a non-word. An idiom is a phrase that cannot be understood unless you know the idiomatic meaning already. "On edge" is an example of an idiom because you are not literally standing on an edge - you are anxious or frustrated.
The question doesn't really make sense - idioms use words the same as any other phrase does. The words communicate meaning to others. The only difference between an idiom and another phrase is that the idiom has a meaning that is not literal and cannot readily be discerned by context.
That expression means that he is conceited, egotistical, pompous or vain.
"Grow homesick" is an idiomatic expression that means to start feeling longing or nostalgia for one's home or a familiar place. It implies a deep emotional connection to one's roots and a desire to return to a place that feels like home.
It's not an idiom. Bees actually do hum, because their wings beat so fast that it makes a humming sound.
Idiomatic expression
"You" is not an idiom. It is a pronoun.
"Idom" is not a word in English, so the difference is between a word and a non-word. An idiom is a phrase that cannot be understood unless you know the idiomatic meaning already. "On edge" is an example of an idiom because you are not literally standing on an edge - you are anxious or frustrated.
Promising is not an idiom -- it is a word. Idioms are phrases.
Think about this and you can figure it out. An idiom seems to mean one thing but actually means another. Does "with regard" mean just what it seems to? Yes, it does. Therefore, this phrase is not an idiomatic expression.
This is not an idiom. It means exactiy what it says - "advanced" means moved up or moved along, so the person is older.
An idiom is a phrase that doesn't make sense until you know the definition. Can you actually fall into a hole called "love"? No, so this is an idiom.
"Beg" is not an idiom. An idiom is a phrase that you cannot understand unless you know the definition. "Beg" is a word that you can look up in any dictionary.
This is not an idiom - it means exactly what it says. The person is so foolish that everyone is laughing at them.
"The cup of coffee" is not an idiom that I know of. It just means a cup full of coffee.
This is not an idiom - it means exactly what it says. You will use any means to achieve your goal.
Which phrase makes no sense? That's the idiom.