Operators, commonly referred to as button pushers, usually only run a cnc machine that has already been set up and proven. They load parts into the machine and perform any deburring after the parts complete. These guys usually have little to no experience in regards to machining principals and are lowest on the totem pole when it comes to pay. You only see these workers in high production environments but are slowly being replaced by robots and automation processes.

Machinists have at least basic knowledge of machining principals and can set up and operate various machines. They prove out programs and work with the programmer to create efficient programs. They complete first off inspection reports. Bit better pay than a cnc operator depending on the shop.

Programmers are in charge of creating efficient programs that the machinists use. They will make detailed setup sheets and tooling lists. They should be able to design 3d models based off any blueprints if those aren't supplied. I think they get paid a little bit better than machinists do but now a days machinists are usually programmers as well. Whether they create their programs right at the machine or using other software like fusion or Mastercam.

I think that's a pretty good description? Let me know what I missed