Okay, I'm not going to be quite so ambitious as to explain everything about both paradigms, just one example that highlights what a major difference is and why it exists.
Today's example: "object" state.
Imagine a small Post-It pad as your memory, with, say, a number "2" written on it. In fact, let's be more "ambitious," and imagine a mini-clipboard, with four post-it notes on the back:
Now, imagine tearing off the "2", writing a "3" on a new note, and sticking the new one in the place of the "2".
To an OOP person, you've just changed the state of an object. To an FP person, you just changed which state the object refers to. The OOP person maintains continuity with the object. The FP person keeps continuity with the values associated with an object. To the OOP person, it's the same object, just with different (new) parts. To the FP person, it's a different object, because it has different (new) parts (it just has the same name as the original object).
It's kind of like marriage: you're still you (OO), you're just now the same as you used to be (F)...