There's no difference in meaning. There are certain verbs - work, live, and study - which have the same meaning in the present perfect simple and continuous when used in sentences such as these. Both mean that you began your studies of Spanish when you were a child and you are still studying it now.

They are almost the same, but there is a very slight difference in meaning or nuance - at least, to my ears. With "I've been studying Spanish since childhood" there is a tiny bit more more emphasis on the fact that you are still studying Spanish now". With "I’ve studied Spanish since childhood" it is not quite so definitive. It suggests like the other that you are still studying Spanish now but it leaves open the possibility that at the present moment you have stopped - perhaps temporarily, perhaps forever.

In the first sentence you finished the study Spanish but it's not important when you did. In the second sentence you still study Spanish. There is ongoing activity.

The first sentence implies that you have stopped studying Spanish at some point, while the second sentence suggests that you're still studying it.