What is the difference between a Shakespeare comedy and a Shakespeare tragedy?

The way to tell if a Shakespeare play is a comedy or a tragedy is to look at the ending. If, at the end of the play, most of the cast is lying on the stage dead, then you are watching a tragedy; if, at the end of the play, everyone is still alive and a whole bunch of people are getting married (or those who used to be unhappily married are now happily married) then it's a comedy.

Some plays are hard to fit into a category. Troilus and Cressida ends with everyone unhappy, the lovers are not married, but on the other hand nobody except Hector is dead. Cymbeline ends with the evil queen dying but with Imogen and Postumus reconciling.

So while you may think that comedy is funny and tragedy is sad, these ideas apply only to modern works, not Shakespeare, as follows:

Modern Definition: The comedy is designed to make the audience laugh and the tragedy is designed to make the audience cry (or at least go very quiet)

Shakespearean Definition: Comedy ends with a marriage, Tragedy ends with a death.
A Shakespeare comedy's plotline is generally funny and confused. Tragedies usually end with the death of every main character.

Tragedy: Romeo and Juliet

Comedy: The Comedy of Errors