A sweeper is any Pokémon meant to either punch large holes in enemy teams early game, or clean up the enemy team in the late-game. That being said, many sweepers can work well with some stalling moves. For an example, a Reuniclus might have Psychic, Focus Blast, Shadow Ball, and Recover, but it would still be a sweeper if its purpose is to damage the enemy team, despite having Recover, a more stally move.
A staller usually refers to a massive wall, meant to soak up hits and slowly beat an enemy with chip damage. However, some stallers can have a terrifying offensive presence, as well. A good example is Hydration Vaporeon, a Pokémon that eats up a multitude of hits on rain teams. Despite its rather okay 110 Special Attack, its Scald or Surf can be strong enough to outright OHKO an enemy Cloyster in the rain, even though it is resisted.
Even so, most sweepers are better off with a very sweepy set, while most stallers are better off with a very stally set. These two are just examples of Pokémon that fit one archetype while having traits of a completely different one.
I hope I helped.