305 was Cessna's model number for the initial design they offered the US military in 1949 to meet a specification for a two seat artillery spotter. The prototype was N41694 which in initial configuration had a short nose cowling. It featured added fenestration to rear and sides to meet the spotter specification. The 305 used the tail of a Cessna 195 and wings of a Cessna 170 on a new fuselage design. First flight was 14 December 1949.
The Military assigned various designators to production versions ordered on contracts and also changed designators after some time, about 1952 or 1956 as I recall. Some examples of Bird Dogs were the L-19, L-19E, TL-19C, O-1, O-1E, and O-2. The OE-2 for the US Marine Corps was a Cessna model 321, so Cessna changed their model names with various upgrades/versions of the Bird Dog. The XL-19 tried a turboprop engine, without ensuing production contract. A diesel engine Experimental version was also tested.
N4443P is registered with the FAA with a Cessna model 305 designation. Suggest you add explanatory information in your photo caption/s or add Military data on the aircraft as allowed on the Aircraft Profile page. It would be inappropriate for you to try to change the registration information unless you are the aircraft owner; and then the FAA would discourage that because of the cost (to you if owner) and hassle. Do you know the equivalent exact military designation? What you have discovered is very common in registrations of former warbirds.