You are correct. The term padmount opens up a whole new set of terms and definitions relating to underground power distribution.
The terms are:
dead-front primary connections (no exposed high-voltage parts, to accommodate rubber 'elbows', with no bushings. Very popular for safety reasons.
live-front: exposed live metal connections to standard primary bushings--we never use these.......deadly.
radial fed primary: high-voltage lines terminate on a single bushing or connection, with no other connection to feed more transformers or circuits.
loop fed: high voltage lines terminate at a connection, with an additional termination to feed additional transformers or circuits at other locations. This is very popular, and the primary purpose of this is in case one of the two primary lines fail, it can be disconnected (for repair) and the transformer can be fed from the other line connected at this point, from another circuit.
The padmounted transformers typically have two separate compartments: a high-voltage primary compartment, and a low-voltage secondary compartment.
You can obtain much more information from ANSI C57 (transformers), as well as rubber elbow manufacturers Elastimold and Cooper Power Systems RTE.
I'm sure I missed a few things, but this is fairly quick and to-the-point summary.