either are good or not a concern but intent is a higher urgency to act immediately and possibly more drastically. Hopefully her doctor is trained to differentiate that and did so but I’m afraid sometimes physicians (or generalist medical providers) are not. It’s important to know more specifically what type of self harm thoughts she’s having (is there a plan? does she have means to enact that plan? Is she future oriented?, etc) but probably best that you’re not the people to ask those questions.

Others have given you good things to think about as well. Best wishes to all of you. Hard, hard stuff.