Yep there are differences.
Here is the T-bird steady rest which is actually called a front support in this case.

Here is the engine side support for the Thunderbird.

Here is the engine support for 54 and up cars

And the car steady rest which I couldn't find in the parts and illustration guide but there is a illustration in the 1956 shop manual I have.
1956 Ford Fairlane Town Sedan - 292 Y8 - Ford-O-Matic - 155,000 mi