General term for someone who makes or manufactures something. Can refer to individuals, companies, or craftspeople.
The maker of this furniture is a famous craftsman.
The manufacturer of that product is still unknown.
Specifically refers to the producer role in film, theater, television, or other entertainment productions.
He is credited as the producer of that movie.
製造者 is more technical and often used for industrial or factory-based manufacturing, whereas 製作者 can be broader and include craftspeople or entertainment producers.
Compound of 製作 (seisaku, 'production, manufacture') + 者 (sha, 'person'). The meaning is transparent from its components.