(I'm a U.S. native speaker.) In the U.S. there is no difference in meaning. There isn't even a subtle difference in meaning. Both are used. "Call" is a more common. One word or the other might have been more or less common in various places at various times. The full phrase is "to make a phone call," so, just guessing, perhaps some people shortened it to "to phone" and some shortened it to "to call."

Yes, it's the same one that's an expression of a way of saying "Call me" or "Call back"

Well "call me" can also be used to mean "give me shout" if the person is within speaking/shouting distance... "phone me" just makes it more specific, use a phone to contact me... "call me" can be used to imply the same thing, since it's called a "phone call"...