The MH, MHT, U-MH, and U-MHT are the crying baby vents. The MMT, MHST, U-MMT, U-MHST, and U-MHU are the baby boomer vents. The crying baby vents all have blue piezos that output a 3000 Hz tone while the baby boomer vents have black piezos that output a broadband tone (or a broadband tone with other tone options).
The names could probably be further subdivided by the generation.
First generation (F-Series): MH, MHT, MMT, and MHST. The strobe models all had vertical strobes to the left of the horns.
Second generation (U series, fixed candela): note that the non-strobe U-MH and U-MHT had the same Faraday model number as the MH and MHT respectively (6300/6301/6310/6311), so they should be named the same. On the other hand, the remote horn MMT and MHST have different model numbers from the U-MMT and U-MHST (6380/6381/6320/6321 vs. 2880/2881/2820/2821), but they look identical and I am not sure how they are even different. All of the strobe models have new model numbers and sharper edges.
Third generation (U series, multi candela): this only affected the strobe models. The main difference in appearance is that the FIRE lettering is written on the side of the second generation models but on the front of the third generation models, since the third generation models were designed for universal wall/ceiling mounting. The U-MHU was also not introduced until this generation.
The remote horns were also available as both single gang and universal-mount devices, which gives more opportunity for naming.
The shrederator seems to have been the origin of the crying baby vent’s design. Perhaps the baby vent was crying because it was scared by the shrederator?
