I recently found out that the phrasings 相手のスピリット1体のコア and 相手のスピリット上のコア are actually significantly different. Probably not a good thing that I only just noticed, seeing as that means the translations are slightly off. But the "remove cores" category is fixed now. Anyway, figured that if I was oblivious to this, somebody else probably was too. So here's a guide to the wording on core removal:
"Your opponent moves" (相手は、相手の) = Your opponent gets to decide where to move from.
"Any" / unspecified number (相手のスピリット上のコア) = You can take the core from the same spirit or different spirits.
When Charged: You can take multiple core from anywhere on the field.
This one I was aware that, when charged, would end up removing from multiple targets, but I didn't know how to phrase it in english. I almost went "A core from opposing spirits" but that's make people think "one from each" so I aborted it