I am not going to comment on if they are different or not. Honestly, I don't care. For my understanding, I strictly use the below :
The terminology, "Parent" and "child" are abstract and can be used for a lot of things especially trees. They are used to describe hierarchy. And that's why it's not wrong to use parent and child for classes/inheritance.
With respect to inheritance, the preferred, correct and non-ambiguous terminology is "base" and "derived".