Yes....you are.
Part 135 is non scheduled charter and air taxi operations.
Basically you call and they show up with an airplane.
Part 121 is
scheduled air carrier operations.
Meaning you have to show up in time to go along on a pre scheduled flight.
Cape Air provides 121 operations in a Cessna 402.
And 135 ops can be in any size of airplane, from a 172 to a Boeing BBJ.
So size does not matter......
Then there is Part 91 operations, which is defined as "owner operated".
Take Coca-Cola for instance, they have a fleet of app 30 jets that operate under part 91 operations. Meaning that every employee of that company can get a ride on the airplane, also invited guests of the company.
They cannot charge their guests though because that would be providing transportation for hire.