Each U.S. Navy (USN) aircraft was assigned a unique designation that identified it's intended purpose, model, series and possible special modifications. The coding system, which was introduced on 10 March 1923, remained in effect until 18 September 1962 when it was changed to the tri-service system based on the system used by the U.S. Air Force.
Designations are:
A; Ambulance (1943-1946) eg Piper AE-1 Cub
[FONT=Arial,Helvetica][SIZE=-1]B: Bomber (1931-1946) eg Douglas BD-1 Havoc[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]BT: Bomber-torpedo (1942-1946) eg Douglas BT2D-1 Destroyer II[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]F: Fighter (1922-1962) eg Grumman F4F Wildcat[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]G: Transport, single-engine (1939-1946) eg Beech GB-1 Traveller[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]H: Hospital (1929-1943; to A in 1943) eg Piper HE-1[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]HJ: Helicopter, Utility (1944-1949) eg Sikorsky XHJS-1[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]HN: Helicopter, Training (1944-1948) eg Sikorsky HNS-1 Hoverfly[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]HO: Helicopter, Observation (1944-1962) eg Sikorsky HOS-1 Hoverfly[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]HR: Helicopter, Transport (1944-1962) eg Sikorsky HRS-1[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]J: General Utility (1931-1946) eg Grumman JF-1 Duck[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]JR: Utility Transport (1935-1946) eg Beech JRB-3 Expeditor[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]LB: Glider, Bomb-Carrying (1941-1945) eg Piper LBP-1[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]LN: Glider, Training (1941-1945) eg Pratt-Reid LNE-1[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]LR: Glider, Transport (1941-1945) eg Waco LRW-1 Haig[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]N: Trainer (1922-1946) eg Stearman N2S-4 Kaydet[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]O: Observation (1922-1962) eg Stinson OY-1 Sentinel[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]OS: Observation Scout (1935-1945) eg Vought OS2U-3 Kingfisher[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]P: Patrol (1922-1962) eg Lockheed PV-2C Ventura[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]PB: Patrol Bomber (1935-1946) eg Martin PBM-3D Mariner[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]R: Transport (1931-1962) eg Douglas R4D-5 Skytrain[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]S: Scout (1922-1946) eg Curtiss SC-2 Seahawk[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]SB: Scout Bomber (1934-1946) eg Douglas SBD-5 Dauntless[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]SN: Scout Trainer (1939-1946) eg North American SNJ-3C Texan[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]SO: Scout Observation (1934-1946) eg Curtiss SOC-3A Seagull[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]TB: Torpedo Bomber (1936-1946) eg Grumman TBF-1C Avenger[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]TD: Target Drone (1942-1946) eg Culver TDC-1 Cadet[/SIZE][/FONT]
[FONT=Arial,Helvetica][SIZE=-1]TS: Torpedo Scout (1943) eg Grumman TSF-1[/SIZE][/FONT]
With the US Air Force the designation "P" was a leftover from the Great War, when fighters of both the French Aviation Militaire and the burgeoning United States Air Service (USAS) were labelled "Pursuit". The British labelled their fighters "Scouts".
The Unites States Naval Air Service (USNAS) didn't operate fighters in that period, but did operate "Patrol" aircraft, hence when they finally aquired fighters they couldn't use the initial "P" as it was already in use. So they went straight to the logical term, being "F".