Yep, to be more simple about descriptions...
Auxiliary cruiser - converted transport or passenger liner with a battery of guns installed. A stop-gap measure, not a match for any large warship. Variety of roles, usually to scare off raiding enemy warships from attacking traffic.
Heavy cruiser - purpose-built warship. High speed, medium firepower, moderate armor. Variety of roles, from ocean patrol and commerce raiding to fleet action. Emphasis on speed, can pursue enemies effectively or run away from bigger ships.
Battleship - Good speed, high firepower, heavy armor. Originally intended to fight in battle formations against enemy fleets for sea domination. Can be used for other tasks, from commerce raiding to heavy shore bombardment.
In Battle of the Atlantic, Germans wanted to use their battleships to attack and destroy convoys from long distance.
Battlecruiser - Good to very good speed, high firepower, lighter armor than battleship
(German Scharnhorst and Gneisenau are sometimes called battlecruisers, but they actually had the armor and performance of battleships but with less firepower). Also originally intended to fight in formations, with emphasis on speed to give them an advantage in choosing firing position.
Corvette - very small warship, very light firepower, light armor. Fairly slow (slower than many subs), intended as cheap escort.
Frigate (or Sloop) - purpose-built anti-submarine escort. Very well armed with all sorts of anti-submarine weapons. Moderate speed (about the same as submarine). Possibly your worst enemy
Destroyer - very fast, often well-armored small warship. Intended for a variety of roles, from surprise torpedo attacks against enemy fleets to anti-submarine escort.
This is in the WWII Battle of the Atlantic terms, mind you.