The first two letters of the above acronyms represented the type of aircraft, with TB being 'torpedo bomber', SB being 'scout bomber', and PB being 'patrol bomber'. The third letter represented the aircraft manufacturer, since multiple companies often produced the same aircraft models in those days.
Under the 1922 Systems Designation (which was used until 1962 when they switch to the Tri-Service system), those 'first two letters' was anything from 1 to 6 letters, and technically could have been more.
The first (optional) letter would designate a prototype or experimental aircraft with Y or X, but only until the aircraft was accepted for production.
The second (optional) letter would be the general type (Fixed-wing (omitted), Airship (Z), Rotary-wing (H), or Glider (L)).
Then the role (which could be multiple letters for multiple roles). So TB actually means it was designed to act as a Torpedo Plane and/or a Bomber. SB means it was both a Scout and a Bomber. PTB is a Patrol Torpedo Bomber.
Next is the Design number, which is omitted if it is the first, and is specific to a given company. The FF fighter is nicknamed the 'Fifi' because it is technically the FIF-1.
Then comes the company code, which is specfic to the builder (not designer). Note that a given aircraft can have multiple designations if it was built by different companies. For example, the Grumman F4F Wildcat was designated as the FM Wildcat when built by GM (after Grumman switched to F6F production). Note that the company code could be changed or reassigned if a company no longer existed or hadn't produced an aircraft for the Navy for an extended period of time. For example, A referred to the Atlantic Aircraft Corp (aka, Fokker-America) until 1932, then Brewster Aeronatical Corp until 1943, then Allied Aviation Corp until 1946, and finally Noorduyn (Canada).
The final part of the designation is the variant, which is usually only shown when discussing that specific variant of the aircraft. It is simply a dash followed by the number of the variant. A minor modification that didn't justify a new variant designation would have a sequential letter after the variant number, hence the TBF-1C is a minor change to the production TBF-1.
Its actually really similar to the IJNAS designation system.
So, because of omissions/optional codes, you could have a short designation like the FF (Grumman's first Carrier Fighter) or a long one like the XPTBH-2 (a seaplane Patrol Torpedo Bomber that never entered production).