The differences between these models are probably more visual than anything else. The TDH-5303AC were originally numbered from 8000-8202 (NYCTA) and 8301-8780 (MABSTOA). These were the first AC equipped buses to be ordered by the NYCTA in 1966. The originally also had the Bus-O-Rama advertising signs on them also. Only about 23 of these were Blitzed. I think they were 5000-5022. The TDH-5303 is a second generation GM fishbowl.
The NYCTA (1968) T6H-5305A came in two different flavors. Some of them had originally had Bus-O-Rama signs and were originally numbered in 883X-887X series. They were renumbered into the 51XX series. Most of the NYCTA T6H-5305A's did not have Bus-O-Ramas and had the conventional standee windows above the regular windows. These were originally numbered in 43XX,44XX,88XX and 89XX series. They were renumbered into the 51XX and 52XX series. These were third generation GM fishbowls.
The T6H-5309A/10A were pretty much identical. They also looked very similar to the T6H-5305A, but they sounded a bit different. I'm not 100% sure, but I think the difference between the 09A and 10A is the location of the exhaust pipe. Both the T6H-5309A and 10A exclusive NYCTA/MABSTOA models. They are 4th generation fishbowls and are identical to the T6H-5307A. There originally 45XX,48XX and 49XX series (MABSTOA) and 60XX-63XX at NYCTA. They were renumbered to 53XX-55XX series.
The codes are P=Parlor,S=Suburban,T=Transit for the first character. Parlor (P) was used for intercity buses. The second character originally indecated the type of engine: G=Gas, D=Diesel. This was later changed to an 6=6 cylinder diesel Detroit Diesel 6V71 engine or 8=8 cylinder Detroit Diesel 8V71 engine. The third character was for the transmission: H=Hydraulic (automatic), M=Manual. The next 2 numbers indicated the seating capacity and length of the coach : 33 (30 feet long), 45 (35 feet long) and 53 (40 feet long). The next two numbers indicated the series and in most cases the width of the coach.
On 40 foot long buses if the last number was odd the bus was 96 inches wide and if it was even the bus was 102 inches wide. On 35 foot long buses it was the opposite. First generation fishbowls used 01,02,16,17 and it indicated 40 feet-102 inches wide, 40 feet-96 inches wide, 35 feet long-102 inches wide and 35 feet long-96 inches wide respectively.
The last character was added with the third generation fishbowls as either an A=Air Conditioned or N=Non Air Conditioned.
The Blitz rebuilds did have A/C. The local buses operated with no A/C for a year when they were retrofitted with roof mounted A/C units.
There were plenty of GM fishbowls that were not "Blitzed". They were pretty easy to spot.
There are some more variations to the model designation codes for the RTS and Classic that I can post if you'd like.
Hope this helps...