It's indeed called the discrete logarithm problem both in the case of finite fields modulo some number and elliptic curves modulo a number. In the first case, you are reversing an exponentiation, so you're indeed computing a logarithm. But in the case of elliptic curves you're not dealing with exponentiation, you're instead reversing the multiplication of a curve element (i. e. a point) by a scalar. The two problems (and the way you solve them) look similar in the end, and I think this is why we ended up using the same name. But, if we nitpick, those are different operations and so the two problems are different, despite the similarities.

Note for cryptographers/matematicians: I know that "reversing" isn't the correct term here, so you could accuse me of the same sin I'm calling out in my previous comment. But it makes the explanation shorter while still conveying the correct meaning in the end.