The four possible patterns with causative "have" and "get" are the following (I will use TRomano's example in the comment above):
- They had us build a prototype.
- They had a prototype built.
- They got us to build a prototype.
- They got a prototype built.
They are all in the active form, but (2) and (4) do not mention the builder and can thus be deemed to include a passive structure.
In (1) and (3) "have" and "get" are synonyms, meaning "persuade" or "order". Besides, according to the Longman dictionary causative "have" in pattern (1) is mainly AmE:
b) to persuade or order someone to do something
have somebody do something especially American English
I’ll have Hudson show you to your room.
- to persuade or force someone to do something
get somebody to do something
I’ll get Terry to check the wiring for me.
We couldn’t get him to sign the agreement.