It seems like "generative" is coming at the art from the "output" angle (something "got generated," implicitly by a means other than the mere "hand" of the human artist); whereas "algorithmic" is coming at the art from the "input" angle (some algorithm was involved in an artistic process).
I think you could have a generative system that wasn't algorithmic -- it could involve analog variables in "nature" that weren't based on a set algorithm. Some fluxus instruction pieces and experimental 20th century audio compositions are "generative," but I wouldn't call them "algorithmic." Burroughs'/Gysin's cut-ups are arguable generative without being algorithmic.
Also, I think you could have an algorithmic piece that wasn't generative. You could simply use a static algorithm without any variable input as part of your artistic process, and it would produce consistent/predictable output that wasn't "generative." It would still be "algorithmic," because an algorithm is just an algorithm.
Note, computers aren't needed to make either "kind' of art. Note, Cage's use of "aleatoric" might be more specific and useful (and speak of the devil: http://en.wikipedia.org/wiki/Aleatoric_music
If you were drawing a venn diagram of the two "kinds" of art (generative and algorithmic), the circles would share a common area, but each circle would also have areas that weren't in common.
Just my thoughts about what it seems like the terms (should) mean, not really related to how they have been used historically by artists/curators/critics. Some artists are very invested in the term "generative," so they can chime in and add their opinions if they are reading.
Generally WIkipedia is not the best resource for the nuances of contemporary art (but a wonderful resource, as Jon Ippolito noted recently, for fan fiction minutiae and obscure underground rock bands).