The Prime swarm is usually the first swarm of the season, but not always, the prime swarm is the largest swarm of the season.
Afterswarms are swarms that occur closely after the initial swarm, they can have either mated or unmated queens.
Cast swarms are an afterswarm that is too small to be of any worth, say baseball sized. They occur at the tail end of a series of after swarms or late in the season.
Remember the old adage:
A swarm in May is worth a pile of hay,
A swarmm in June is worth a silver spoon.
A swarm in July isn't worth your time.
A swarm in August should be cast away.
Swarms with multiple queens are not all that unsusual, and it is possible for a swarm with multiple queens to throw a cast swarm shortly after setting up housekeeping.
I've known of hives to throw as many as 15 afterswarms in one season, all but the 1st 2 or 3 were cast size (small and worthless)
Often the original queen will have swarmed days prior to the successor queen's hatching (which is why you can end up queenless if you remove capped queen cells).
Sometimes queen cells are developed over a period of a week or 10 days. Not all the queen will hatch at the same time, and subsiquent hatching will produce after swarms. A newly hatched queen will only kill those queen cells that are piping or where she hears a queen eating away the cap. Queens cells holding queens that havent developed to that point are ignored, setting up the possibility of a mated queen after swarm.
In the case where 2 queens hatch at the near the same time, and do not come in contact with each other, possibly with both going on mating flights and then one swarms when the come in contact (it is also possible it could remain a 2 queen hive).
It is also possible for a later developing queen to hatch and exit the hive on a mating flight while the queen that hatched rior to it is on one of its mating flights.