A
short
drain is needed if you already have plumbing installed and
just need the top part that goes inside the sink. Short drains are
normally used when you have an enclosed vanity that no one will be
able to see underneath.
A
full drain includes the P trap or Bottle trap
and all plumbing that would normally be under your sink. Our full
drains are manufactured to be aesthetically pleasing. Full drains
are used when your vanity is open underneath and you would be able
to see the plumbing.

It is a dran for a sink with a built in overflow.