What are the important differences between Part 121, Part 135, and Part 91 operators?
So loose guidelines to match the loose question...
Pt 91 - generally private flying. That is, no flying an airplane with paying customers unless those customers are government officials on government business. This rare exception is called "public use"...it gets more complicated but let's leave it at this for now.
A rich guy who owns a jet to fly around in (or a company that owns a plane for business use) can be pt 91 as long as they don't sell seats or cargo space to the general public.
Pt 121 - scheduled commercial air service with paying customers. Planes are flown on defined routes as often as the operator wants. This is where companies like Delta and American operate.
Pt 135 - on-demand and scheduled charter. When you call a company and say "take me (or my freight) fom LA to NY" you are likely talking about a pt 135 unscheduled charter. "Scheduled" charter is allowed but is limited to a few days a week (four, I think).