The most "basic" form of weight training is to do your desired amount of sets for one body part, and then move on to the next body part.
You can't "necessarily" judge what a trainer does with a client with what you should do. There can be far to many different variables involved between you and the person the trainer is training.
Personally, I strictly time (through a stop watch) all time between sets (TBS), as I view this period as with many other logistics within weight training as one element among many that can be used to increase intensity, assist with breaking plateaus (of reps, etc), and an area to facilitate muscle growth/strength (considering diet equal here) if manipulated correctly.
Sometimes, persons within weight training become too narrow minded when confronted with problems when training,
when in fact they utilize and perform the very things that can be used to iron out the complication they may be experiencing.
Therefore in its most basic format (not adding in any advanced methods), you would peform sets of squats, and then move on to do sets of Dead Lifts, as an example. The Time between Sets (TBS), can depend on a persons goal, rep ranges, etc (and experience), but tradionally its between 1 to 3 minutes (approx), with some taking longer dependent on goals.
Here is an article on rest periods:
Bodybuilding.com - Topic Of The Week - What Is The Optimal Time Between Sets For Muscle Growth?
Best of luck in all that you do! ROCK IT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Chillen