I was a dealer for all these machines in the old century as well as a constant user of them. The general evolution was-
3340 with the manual cue lever for functions.... like driving a garden tractor
3340s, logic control of the transport functions (ie, silver lever dumped)
3440, further logic improvements but keeping the "Teac" name for the model
40-4... last to use the "Teac" name . Was basically a 4-channel version of the 80-8 and continued to use the original, increasingly complained-about style lifters/tape path configuration. No pitch control
............... end of series that utilized all ac-motors ....................
44, appears with Tascam brand name instead of Teac, incorporates the logic monitor switching of 80-8, 90-16, 85-16, including ability for machine to stop at zero, rather than running off the reel. A dc motor is finally utilized to (sort of) overcome the frustrating speed/pitch deviation that plagued earlier 33** models in high heat conditions and speed/pitch issues of music at head of tape compared to at end areas of tape. IE, it was difficult to say, razor blade a take edit from something recorded at the end area of the reel and then splice it onto an earlier area because of minute pitch deviations. The 44 though, was still using the almost antiquated tape path scheme as the 3340. The rare, optional external varispeed box you could buy to add pitch to an 80-8 was now integrated (technology-wise) to the 44 to give it varispeed. Instead of the old dolby boxes you could buy for the 33** series, the 44 included the option for dbx units that bolted on... similar to the way it had been done the previous 3 years for 80-8, 85-16 machines and then ms16. The addition of the dc capstan motor (although still belt driven) technically now allowed external sync. But there wasn't really mainboard design factored in for it.... at the time, I felt Tascam didn't really care as they figured no one would use the machine in ext sync with a second machine just to use 3 tracks.
44-ob was a major revision to update the 44. The machine was now on par with the ms16 and even the atr models imo. Full external sync was built in, 3 dc motors, adoption of the transport path of the pro series (ie, dumping the 3340 approach), including full tension servo control for very stable pitch from beginning to end of reel, xlr I/o in addition to rca, better integration of logic switching for optional dbx, very heavy chassis to handle all-day shuttling of tape for edits/sync etc. Plus a few other little odds and ends like the splicing block.