Causative - Passive/Active voice

The four possible patterns with causative "have" and "get" are the following (I will use TRomano's example in the comment above):

1. They had us build a prototype.
2. They had a prototype built.
3. They got us to build a prototype.
4. 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.

22. 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.