There are three main reasons why you guys are confused about this. First, because you don't know what these titles really mean. Secondly, because whoever you've heard speak on this before probably didn't know what the fuck they were talking about. And third, because a lot of people perform more than one job in the studio. I'll try to keep this as simple as possible and we'll start with; fuck what you've heard or think.... Now..
A COMPOSER composes music. If you make beats, you are composing music. You are a composer, not a producer.
A PRODUCER guides the production of a song and has *SIGNIFICANT INFLUENCE* on its FINAL outcome. Meaning, they make fundamental decisions regarding the different elements of a song, which result in a completed piece of work.
An ENGINEER (recording engineer that is) is responsible for the actual hands-on recording. The engineer is the person who sets up mics and presses record/stop. Good engineers will offer suggestions and their opinions but by no means does that make them a producer. Unless, as I stated earlier, they've had *SIGNIFICANT INFLUENCE* on the outcome of the song.
These definitions ARE NOT negotiable and they DO NOT CHANGE. It makes NO DIFFERENCE whether you are doing rap, rock, jazz, pop, country, gospel, folk, or whatever the fuck.
If you're still confused then slap yourself a few times, take a deep breath and read again. Repeat this process until you get it! lol