I feel like eating an apple =I want an apple Are there any differences?
Sure, there's a difference.
Feel like - is used to talk about how you feel, not what you want.
Want - is used totalk about what you want, not what you feel or feel like.
However, in common, informal usage they both would be interpreted as:
'I want to eat an apple' or ''I feel like eating an apple.'
You could also just say 'I feel like an apple' and no one is going to take that literally. Who even knows what it feels like to be an apple?
So, language can be very imprecise and still communicate, especially when it is spoken casually or informally.
If you were to analyse these sentences you would see that they have real syntactical differences. These sort of things matter most when you need to be precise so there is no ambiguity in what you are saying.