I wrote this up since people kept mislabeling transmissions in their cars and it drove me nuts. Anyway, I wanted to share it all with you guys. Don't yell too much if I screwed something up... it's a LOT better than what I've seen over there...
Wow... lots of wrong numbers here... I will help with my knowledge of vintage FWD Chryslers.
A413 is what's used in any 4 cylinder FWD Chrysler with a Chrysler made engine from 1983-2001 with a THREE SPEED AUTOMATIC.
The original version had three clutch packs and did NOT have a lockup torque converted, this was added in 1987 for the TBI FWD Mopars.
A beefed up version came out in 1984 for the Turbo FWD versions. The beefed up version gained a lockup torque converter in 1991. I think it had 4 clutch packs and other better internals instead of the 3 the TBI car trannies had.
The Neon came out in 1994 and had the same internals as the Turbo A413 with a different bellhousing for the Neon's 2.0 engine instead of the 2.2/2.5 family of the K based cars and vans. It had a lockup torque converter.
The A470 is a standard A413 with a bellhousing to match the Mitsubishi 2.6L crapengine that was put into the K based cars and vans until 1987. No lockup torque converter.
The A670 is a turbo internal version of the A413 with a bellhousing to match up to the Mitsubishi 3.0L V6 used in the K based cars and vans. It had a lockup torque converter.
The NON LOCKUP CONVERTER transmissions can be used with Dexron II or III. LOCKUP CONVERTER transmissions SHOULD use ATF+3 (aka Type 7176) and now enjoy ATF+4. Using Dexron can and probably will cause lockup shudder and possibly failure. Plus, the ATF+4 (in my opinion) is a superior fluid that's made specifically for Chrysler transmissions. I hate GM junk and don't want their crap Dexron in my automatic Chryslers.
For future reference (and because it might pertain to something someday around here)...
A404 was the original FWD tranny Chrysler had in their 2.2L and 1.6L/1.7L cars. All the cars that used it (78-82 Omni's and 81-82 K cars) should all be crushed and scrapped by now so I wouldn't worry about it. If you have one, the later A413 is a direct swap in case it dies... and congrats for keeping rust from eating it alive.
A460 is the original FWD 4-speed manual transmission from 78-85. It is rod shifted and pretty weak internally.
A465 is the same as the A460 but with a 5th gear added to the unit. Used till 84. Junk.
A525 was a 5 speed manual used from 1984 on all cars till 1987. Then used on L bodies from 87 until 1990. Chrysler needed this tranny to handle turbocharged power and it was still rod shiftable so that's why it stayed in the L bodies until they were canned.
A520 was a 5 speed manual used from 1987-1989. This was the standard transmission on all TBI and non-intercooled K based cars and was a decently stout and reliable tranny.
A555 was a very similar transmission as the A520 but had a Getrag gearset for enhanced reliability and a more stout 4 pin differential for "agressive launches" according to Ma Mopar. 87-89 Turbo II and 89 Turbo Caravan was where this was found.
A523 was a refined 5 speed manual for everything but the intercooled turbo cars that had a MUCH improved shift quality and better quality parts than the older models. This was used from 1990-1995 on the K based cars and vans.
A568 is the Getrag version of the A523. Hailed by the Turbo Mopar croud as the best FWD manual for the K based vehicles. Used on the 1990 Turbo IV (VNT) and the 1991-1993 Turbo III (16V DOHC) K based vehicles as well as the 1990 Turbo Caravan.
A543 was the same internally as the A523 but with the bellhousing to fit the 3.0L V6 engine that was offered in certain models from 1990 to 1994.
A578/T350 is the Neon manual transmission.
A???/T850 is the SRT4 manual transmission.