A desk is a type of table that you use to do office or school work on. It often has drawers attached to it for storage. You can also have a computer desk. Basically, a desk is for working at.
A table is not usually used for working at (although you might have to if you don't have a desk, for example, a child may do their homework sitting at a kitchen table but that doesn't make it a desk~). Some types of table: dining table, kitchen table, side table, coffee table, occassional table, trestle table etc.