First, we need to differentiate between the pre-62 and post-62 transmission designs.
OK, we have pre- and post- but what about the 62 itself?
Transmissions were slated for revision for the 1962 model year, but as we know, there was almost always some carry-over when Chrysler Corporation made changes…”use up the parts we have boys, don’t be wasting anything”…or perhaps something like that.
Transmission changes, for all applications, were a result of changes to the engines, specifically, the crankshaft flange.
We don’t know exactly what caused the changes to be made, we only know that the flexplate driven torque converter was here to stay. The slant 6 was released in 1960 and part of the new design was the use of the flexplate. Perhaps MotherMopar used the two intervening years to test the design before changing the v-8’s.
So why did they also change the block bolt pattern? Again, no information, but likely a barrier to swapping the transmissions and the resultant carnage it could create.
Prior to the change-over, all of the Early Hemi engines, the Hemi-based Poly engines and the new-for-1956 ‘A series’ engines all shared the same block bolt pattern. All engines, except for the ‘new’ slant 6, shared the same crank flange design prior to the 1962 change-over.
In the 1962 model year we have found both styles of the engine/transmission combination so you must identify the transmission before attempting to use it, rather than rely on the vehicle being a 1962 model.
The late 62 and the 1963 and 1964 TF used a PushButton shift arrangement similar to previous models but with the addition of a ‘Park’ feature. The 1965 TF was similar except that it morphed into a cable shift style such as was used in previous console shift cars. These system are not interchangeable due to the length and design of the ‘drive end’ of the cable itself. The other important change at this point is the new for 1965 slip yoke on the propeller shaft replacing the ball and trunnion design. Remember this part: If you want a PB shift with a slip yoke then you need to install a 1964 style valve body and cable system in the 1965 transmission.
The other option is to remove the drive flange from the pre-65 transmission and install a u-joint yoke and then fabricate a driveshaft with the slip-yoke. This design has been used in many application including Dodge pickups such as the 2005-2008 1500 series with the Getrag 238 6-speed transmission. This transmission is noted in the Manual transmission section.
So, the next often asked question is whether or not you can use the smaller A-904-998-999 series transmission. Short answer is NO. Once again, we are left to speculate on the reason for the slight design variation between the two transmissions, but the fact remains that the A-904-998-999 has the starter mounted about ½” higher compared to the larger 727. The small change in position causes the starter to hit the block on an EarlyHemi or Hemi-based Poly. There have been successful projects using the smaller transmission but the block adapter must be designed with the starter position in mind and the transmission bolt pattern and alignment dowels must be rotated CCW to effectively lower the starter location. The amount to rotate will be a function of providing adequate clearance from new holes to old holes unless a new adapter is machined with only the rotated pattern. Considering the cost to fabricate a new block adapter or to modify an existing product, it may be more cost effective to simply use the 727 with the added benefit of having a more robust design in stock form. Remember that the 727 is, internally, essentially the same for all small and big block applications and that the aftermarket has a nearly unlimited supply of repair parts for all 727 rebuilding requirements.

Here is a link to a very good TF identification posting.

The TorqueFlite transmissions have an ID code cast into the housing just below the starter pocket
A-727-A = Small-block
A-727-LA = Small-block
A-904-A = Small-block
A-727-B = All B and RB engines.

These are often difficult to read, especially if the case is dirty. These raised letters/numbers are somewhat thin and not very bold.

If the ID code cannot be read then look at the shape of the oil pan

An additional method to quickly determine small block vs big block trans is the bolt arrangement for the inspection cover. The B&RB transmissions have 4 small bolts on the lower portion of the bell holding the inspection cover.