Pan shapes are the easiest way to ID transmissions. I've included a link that should help.
Most FMX/MX/Cruise-o-matics have aluminum bell and tail housings with an iron main case in the middle. They debuted in the 50's. These work okay. Use one if you have to, but they are not the toughest thing going. Earlier models lack the ability to shift manually.
C4's came out in 1964 (thus the name). They were designed for small blocks and can be rebuilt quite stout, but still a bit undermatched for a Galaxie with decent torque. To my knowledge, all aluminum and with removable bellhousings. All 64's and early 65's are 5-bolt pattern as are the corresponding 289's. Late 65's and up use the familiar 6-bolt pattern.
C6's came out in 1966 (again thus the name). The were designed for big blocks in big cars and light trucks. In stock form they are tough. Properly built, the engine will blowup before they do. The bellhousing is cast with the main case in aluminum. There are three patterns: round FE (352, 390, 428),
squared big block (400, 429, 460), and the small block 6-bolt (late 289, 302, 351W, 351C).
Later C4's and FMX's, and all C6's are "Select-a-Shift". That is 1= 1st lock, 2= 2nd lock, and D= 1 2 3 fully automatic.
AOD are Automatic OverDrive and came out in 1980 I believe. They are a four speed, with 4th being the overdrive. They use a special locking torque converter. They are most commonly found behind small blocks of the early 80's to early 90's. Units later than that need a computer to run. These are great for gas mileage but will shred if abused.
For my money, I prefer C6's, usually backed with a 2.75 or 3.00 rear gear for mileage. Just my experience.