Technically a f2p deck can have any value to it, but a budget deck always has to be "cheap". But if you are putting a f2p deck together that is expensive, I would say a good thing is to clarify why you call it a f2p deck.

For like 95% of all intents and purposes they could be considered the same. At least in my book.

There might be some hardcore f2p players that would consider any card that you can not get as a drop from grinding, like old expansions, to not be f2p. But I would say that is a bit hardcore. At least in my book.