So there's autotrophs and heterotrophs, which has to do with where you get your carbon (C atoms). If you're an autotroph, you can transform (or "fix") inorganic carbon (like in CO2) to organic carbon, which are molecules that contain hydrocarbons or hydrogen-carbon bonds. Heterotrophs can't do that. They have to consume organic carbon to use it.

This is what determines if you are a primary producer or not. If you are an autotroph, then you are a primary producer. If you are a heterotroph, you must consume other organisms to get your carbon and are a consumer (note that there are primary consumers, who consume primary producers).

Then there's where you get your energy. If its chemicals, then you're a chemotroph. If its light, then you're a phototroph. If its both, congrats, you're a mixotroph.

You can mix these up. You can be a photoautotroph that gets your energy from the sun and fixes carbon. Cool, you're probably a plant or cyanobacteria. You could also be a chemoheterotroph that must consume your carbon and obtains energy from the chemicals you consume. Dang, you're probably a human.

Chemosynthesis and photosynthesis refer to autotrophic processes so they are primary producers. But the reason isn't because they utilize chemicals to get energy, its because they fix carbon in the process.

Sorry for writing this all out. I'm trying to procrastinate. Thank you for your help.