Should peer review of conference proceedings be listed in a CV with journal peer reviewing, or should it be separate?

A service section would be appropriate, optionally with sub-sections including editor, editorial board, and PC, for instance. Service goes beyond peer-review, so you could also have sub-sections including examiner, for example.

Maybe you can go with a broader heading so you can group them all together - something like "Manuscript Reviewing" will cover a myriad of publication categories, like conference proceedings, journals, edited volumes, etc. EDIT: Would also add that in doing so, the reader would then automatically know that those are all peer-reviewed venues.