I think it needs spelling out a bit just who exactly does what within an environment such as these.
Anyone can be a ticket shop.....you, me or anyone else. No licence, no anything. HOWEVER, whilst you might be selling tickets, you can't use an aircraft in that case for financial gain from Joe Public as you are not licenced to fly for reward (even if you owned your own B737) UNLESS you have a suitable AOC. Therefore, the Trading company / Airline name /ticket shop (call it what you like) has to hire in fully approved "operator with an AOC". ie Maersk (operated by BA) etc etc Manx2 = Vanair, JXT = Jetstream Executive Travel Ltd. THEY ARE ONLY THE NAMED OPERATOR.
However, if you check, Jetstream Express is the trading name of a company called Business Executive Airlines Ltd which has directors and shareholders just like any other business. Jetstream Executive Travel MAY be a shareholder / director though of the 'Trading' company ie Manx2 / JXT.As MUFC Fan says it is all on the websites of both companies.
Just to explain futher, anybody could also OWN the aircraft. JXT, the owners of 'BEA Ltd' or anyone else for that matter. In this case if you look at the CAA files, you will see the aircraft for JXT are owned by 2 different people.
Hope that helps make things a bit clearer.