Is there anything diference between them?
Native Japanese speaker here. "食べる物" is a phrase and is totally different from "食べ物". "食べる物" means "something to eat"; there is a noun and a verb in that phrase. On the other hand "食べ物" generally means "food", and it's considered one word.
Same with "飲み物" and "飲む物"; "飲み物" is one word meaning "drink", and "飲む物" is a phrase, meaning "something to drink".
If you're ever stuck on whether you should use 食べ物 or 食べる物, I think it would be safest to go with 食べ物, or search it up on the spot because different situations require different types of phrases.