(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."