Let’s take a step back and look at “fleet boosts” first. A fleet boost is a buff to the ships that have joined together to form a fleet. There are a variety of boosts available that improve the fleet in various ways. To generate the boost, one player will need to train up skills which unlock the boosts, and that player will need to be in some sort of leadership position in the fleet. There are some ship modules called “Command Burst Modules” which generate the fleet boost for the fleet, but there are limits on which ships can use these modules.
So, in the context of a mining fleet, the three key ships for boosts which improve mining performance are all from the ORE faction. The ships are the Porpoise, the Orca and the Rorqual. The Porpoise and the Orca can be used in any area of the game, hisec, losec and nulsec. The Rorqual can only be used in nulsec AFAIK.
These three ships have special bonuses to make a fleet boost more powerful but the person piloting the boosting ship must have trained the correct skills for the boost to work. If the person piloting the boosting ship has not trained the skills to unlock the boost, the fleet does not get the boost. When other players join a fleet with someone in one of these ships (who has trained for boosts), the other fleet players get boosted. In a mining fleet with mining boosts active, the mining ships all mine ore faster and may be buffed in other ways as well.
The Orca and the Rorqual also have a large amount of ore storage space inside them, so what happens is the mining ships mine the ore and when they are full, they “jettison” their ore into space inside a “can” (you don’t need to bring any cans, they are created automatically when you jettison your ore or cargo from your ship). The Orca or Rorqual will normally have some tractor beam modules fitted and use them to pull the cans of ore to itself, then load the ore inside it’s ore bay. The mining ships can keep mining with minimal interruption, until the Orca or Rorqual has filled up it’s ore bay, then it needs to unload the ore somewhere, usually by docking at a station. The Porpoise can do the same thing but it’s ore storage space is not very large, some mining ships can hold more ore than a Porpoise can.
I haven’t dealt with salvaging players so I really can’t say much about them.