Just to add to what Mark wrote. FAR 119 is the regulation that defines what 121, 125 and 135 operations are, what "holding out" is, and in what situations FAR 119 (and thus 121, 125 and 135), do not apply. FAR 119 (e):
"Except for operations when common carriage is not involved conducted with airplanes having a passenger-seat configuration of 20 seats or more, excluding any required crewmember seat, or a payload capacity of 6,000 pounds or more, this part does NOT apply to-
(1) Student instruction;
(2) Nonstop Commercial Air Tours....
(3) Ferry or training flights;
..."