Well, what was told to your dad was half right. There are 2 variations of the C4. Neither one is an OD unit. The ford OD is normally referred to as an AOD (automatic Over Drive).

There is the standard C4 normally found in a majority of passenger cars which can be identified by the dip stick tube going into the transmission case.

There is also the other unit which is often referred to as... large case... step case...or truck because that's where the majority though not all are found. This C4 can be identified by the dip stick tube going into the tranny pan and being held on with a large compression fitting which must be removed to drop the pan. The larger case tranny is purported to be slightly stronger than the standard tranny.

The two tranny use a different flex plate with the large case taking a bigger unit.

Just in case you happen to run into it there is also one other variation of the standard C4 and that is the one found in the 75-8 V8 Mustang IIs. The tranny is the same, but the IIs used a smaller bellhousing, torque converter and flex plate which is unique to the IIs.

The other thing you need to watch out for is getting the flex plate to match both the tranny your using and the engine. 68 thru 82 (?) 302 used a 28 oz imbalance and 83 up used a 50 oz. Using the incorrect flexplate will result in severe engine imbalance.