I am having a very hard time getting a straight definition of what Part 121, 125 and 135 are.That is, how can I categorize an airline in what part?Except as provided in paragraphs (d) and (e) of this section, each person described in paragraph (a)(2) of this section shall comply with each applicable requirement of part 121 of this chapter on and after the date on which that person is issued a certificate and operations specifications under part 121 of this chapter. Unless paragraph (e) of this section specifies an earlier compliance date, no certificate holder that is covered by paragraph (a) of this section may operate an airplane in 14 CFR part 121 operations on or after a date listed in this paragraph unless that airplane meets the applicable requirement of this paragraph: but as you can see it gets involved (1) Nontransport category turbopropeller powered airplanes type certificated after December 31, 1964, that have a passenger seat configuration of 1019 seats.
Part 135: Commuter, on demand and air-taxi operations. So a charter airline flying 737s would be Part 121 and not Part 125, correct? due to the 737 having greater than 30seats, it would be part 125 unless the operator has obtained operations specifications under 121 then it would be required to be operated to 121 standards-however I don't think that it could be operated under 135---but in general only one air carrier certification is given by the FAA-which would logically be the most restrictive operation undertaken by the operator...
At one time Part 135 "reverse defined" a DC-3 as the largest aircraft that could be operated under 135.
It talked about an aircraft that could carry 7,500 pounds 186 miles with 350 pounds of engine oil. There can be 135 Ops Specs covering smaller aircraft and 121 Ops Specs covering larger aircraft.
The aircraft are listed on the Ops Specs and would not move between them.
Pilots could fly both as long as they had completed both training programs.
Thus, for private operators we have Part 125, while for charters we have 121 Supplemental status, which essentially establishes any charter operator that flies airliners to, in fact, be an airline minus a regular schedule.