The term Sune; (soon-ay), was coined by Lars Petrus for his method, and is the most widely recognized name for the sequence of moves and the case. Sune is a male name in Sweden and is a iron age form for 'the son', in mordern Swedish that is 'sonen'.
The mirror/inverse alg/case is named Antisune (or Anti Sune). Using double layers for the first and last moves it is called a Fat Sune (r U R' U R U2 r').
The Sune is most canonically written as R U R' U R U2 R'
There are many algs related to and/or derived from the Sune, such as its inverse, the Anti-Sune.
Usage of the algorithm: Most often as an OLL in the Fridrich Method or a CO for any cube, but also as a COLL in the Vandenbergh-Harris Method, a CLL, a ZBLL, and besides that you can use it to to do 3-cycle edge permutation if corners are ignored, and more.
All cases of the last layer that has three corners twisted is a 'Sune case'.