A Sweeper is a Pokemon designed to hit as hard as possible as fast as possible. They can be focused as a physical attacker with their Attack, like Blaziken, or they can be a special attacker with their Special Attack, like Alakazam. However, they are usually very fragile, and can almost always be KO'd by a Super Effective attack.
A Tank is the opposite. They are built to take as much damage as possible. They usually are equipped with recovery moves/items to restore their health, or moves/items that increase their defense stats. They usually are lacking in direct attacking ability, but can usually inflict some kind of status effect like Poison, Toxic, or Burn to sap the opponent's health. One of the most obvious examples of this is Ferrothorn. Great health pool and Defense with workable Special Defense, and is able to learn Toxic and Leach Seed. It's ability is also very good for a Tank, causing any Pokemon that comes into contact with it to take damage.