Technical detail, from a Military Historian:
The acft. names and designations are all correct -- Japanese acft. of the period had upwards of three different designations, and the Army and Navy each had its own designation system.
The Army used: the Kitai (Ki-), or airframe number (gliders also received a Guraida [Ku-] number; the Kayaba gyrocopters received a Kazagurama [Ka-] number); the Type number, describing the unit's function, and the year of acceptance (in the Japanese calendar, of course -- so "1940 AD" was "2600"); and once The War kicked off in earnest, popular names were devised, as using designations was thought to give too much info to the enemy.
The Navy used: Experimental Shi numbers, the number being based on the year of the current Emperor's reign (7th year = "7-Shi"); the "short designation", which used: [letter indicating unit's purpose][number of acft. for that purpose which had been ordered][letter indicating builder of unit][number indicating how many models of that unit had been created][lower-case letter indicating minor modification variants] -- plus, if a unit had been designed for one purpose, but converted to another, the end of the code would have a "-", followed by the letter indicating the purpose to which it had been converted; the Type Number, similar to the Army system (tho' "2600" was rendered "0" in the Navy, where the Army used "100"); and the popular-name, where units of a given purpose received "themed" names (carrier and seaplane fighters: Wind ["pu" or "fu"]; interceptors: lightning ["den"]; night-fighters: light ["ko"]; attack: mountain; recon: cloud; bombers: stars ["sei"] or constellations ["zan"]; patrol: seas or oceans; transports: sky; trainers: tree, plant, or flower; everything else: landscape effect). There was a fifth Navy system, the Service Airplane Development Program number, but those files got blowed up....
The above explains why the Western Allies created the unit-naming scheme most of the world is familiar with -- male names applied to fighters and recon floatplanes; female names to bombers, wheeled recon planes (land- or carrier-based), flying boats, and transports (transport names all starting with "T"); tree names to trainers; bird names to gliders.
So, for ex.: The "N1K1-J _Shiden_Interceptor" -- it started like as a IJNAF floatplane fighter [N-], the first (and, as it happened, the only) of its kind [-1-] ordered from Kawanishi [-K-], and the first model of its kind [-1]; when the War showed floatplane fighters were obsolete, the design was converted to a landplane and redesignated as an interceptor [-J; also "Shi*den*", or "Violet Lightning"; the floatplane was "Kyo*fu*", or "Mighty Wind"].
Meanwhile, the "A6M2b Type 0 Carrier Fighter" is more straightforward. "A" indicates "carrier-based fighter"; "6" is the 6th carrier fighter the Navy ordered; "M" is Mitsubshi, the constructor; "2" is the second model of A6M built; "b" indicates a subtype of "A6M2". "Type 0" indicates the unit was accepted in Year 2600 of the Japanese calendar, or 1940 AD. As this unit predated the War going worldwide, no popular name was ever attached; unofficially, the type was referred to as "Reisen" ("Zero Fighter").
Conversely: the "Ki-44 _Shoki_ Type 2 Single-Seat Fighter" was an Army design, intended to deal with enemy long-range heavy bombers operating from China and islands south. "Ki-44" indicates the 44th airframe the Army requested, in total. "Type 2" means it was accepted in 2602 of the Japanese calendar, or 1942 Gregorian. (The reference to it being "single-seat" is to prevent confusion with the Kawasaki Ki-45 two-seat fighter accepted the same year.) The name "Shoki" ("Devil-Queller") is the "popular name".
The "Ki-43 _Hayabusa_ Type 1 Fighter" is much simpler: 43rd airframe ordered; accepted 2601 (1941 AD); "_Hayabusa_" ("Peregrine Falcon") for simplicity.
Always does my heart good to see when people Do The Research.... :)