Perlin noise is a computer-generated visual effect developed by Ken Perlin, who won an Academy Award for Technical Achievement for inventing it. It can be used to simulate elements from nature, and is especially useful in circumstances where computer memory is limited. (See the complete Perlin Wikipedia article.)
Simplex noise, on the other hand, is a method for constructing an n-dimensional noise function comparable to Perlin noise ("classic" noise) but with a lower computational overhead, especially in larger dimensions. Ken Perlin designed the algorithm in 2001 to address the limitations of his classic noise function, especially in higher dimensions. (See the complete Simplex Wikipedia article for more.)
The loise project stated life as a port of the Racket noise-generator by jpverkamp to LFE. However, it has undergone some seriosu refactoring since then, as well as the inclusion of many new features.