"Have" and "make" have different meanings based on the intent, so context is very important, and there will be people who use them interchangeably.
to make someone do something
is to force them against their will to do something with prior intent and is synonymous with force
I made the kids eat all their vegetables.
I forced the kids to eat all their vegetables
to have someone do something
is usually less forceful than being "made" to do something and can be synonymous with ask
He had me wait since the delay made him late.
he asked me to wait since the delay forced him to be late
What... had you do that?
what had happened to cause you to do that
is understandable, but not really used. More often it's said
What caused you to do that?
What made you do that?