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Are they all struck several times and trimmed? Or is this just for progression or process sets?
Coins are not made this way. They are struck within a collar that has any lettered edge or reeding right on the collar die itself.
Most high-relief medals require being struck multiple times in order to fully bring up their design. The process set demonstrates how more and more of the detail is brought up with each strike. With modern presses and planchet preparation techniques, it's possible that fewer strikes are needed, but multiple strikes are still the norm.
Traditionally, many high-relief medals were struck without a collar and required trimming (not just those for process sets). Some were, however, struck with a collar; the collar eliminated the need for the trimming step.
Collecting history one coin or medal at a time! (c) commems. All rights reserved.