What is the difference between a commercial operator and an air carrier? What certificates do you need for both? I saw somewhere online that you need an operating certificate for both air carrier and commercial operator, but then when do you need an air carrier certificate?
In broad general terms, "commercial operator" just means an operator who works for pay. This could be a crop duster, flight school, or major international airline. (Not limited to aviation, a backhoe operator meets this definition...)
An "air carrier" is an operator who carries things by air - passengers or cargo.
Every air carrier is also a commercial operator, but not every commercial operator is an air carrier. The specific FAA operating certificate required depends on factors beyond these basic definitions.
For example, a flight school could be certified under part 141, or could offer instruction under part 61. An airline offering scheduled passenger service would need an operating certificate under either part 135, or 121.