What's the difference between a Euchre, a March and a Set?
Calling and getting all five tricks is A March. 
Calling trump and failing to get 3 tricks is called a Euchre.


This is the earliest reference I could find to Euchre, in Hoyle's 1845 edition.




This excerpt is from The Law and Practice of the Game of Euchre by Charles Henry Wharton Meehan.  Written in 1862, per Wikipedia, it is believed to be the oldest book dedicated to Euchre.



Hoyle's 2001 edition uses the same terms, as does Scarne's Encyclopedia of Card Games.  Card Games for Dummies does as well, however they use the terms "Marches or Sweeps" for getting all five tricks.

While I've heard the other two terms, it does not seem that they have entered common enough usage to be documented into any formal listing of rules.