To me, the word "groove" doesn't point to an specific style or genre. IMO, it's about all those little (or maybe not so little) nuances in your playing that move your audience (like making them feel like dancing). You can play a bunch of notes in the right place, with a good tone and in tune, but if your playing is lifeless, there's no groove. I always quote
Link Removed as an excellent example on groove (Paul McCartney on bass). The notes are very easy to play, but giving them the groove that Sir Paul puts on them may be a really tough call for more than one player. James Jamerson, Jaco Pastorius, Bernard Edwards and Francis Rocco Prestia are other terrific "groovy" players. For examples of great groove with a minimalistic use of notes, I'd say Tony Levin and Donald "Duck" Dunn.
"Funk", instead, is about a style of music which features a solid 4/4 beat with heavy syncopations played over that. There are other key components, but for a brief description I think those two are the most important. Tower Of Power (with Rocco Prestia on bass), Rose Royce (Lequeint "Duke" Jobe), Red Hot Chili Peppers (Flea) are just a few examples to check.
I think now of a phrase that summarizes my point of view on this difference: "You can groove with no funk, but you can't funk with no groove" (did anybody say that before?

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