There is little that is more frustrating than trying to make sense of the various names of olives. Some names refer to the variety of tree (Picholine) or the area from which the olives come (Nicoise); some refer to the method of preservation (oil-cured) and some refer to the flavoring mixture (Provencal--with rosemary, thyme and lavender). The best way to choose an olive is by tasting.
In general, black olives are ripe and have developed, complex flavors. Green olives are unripe and tend to taste fruitier and a bit more lively. It's like the difference between raisins and grapes. Dry-cured olives tend to have a deeper tang and to be less exuberantly salty than brine-cured. Green olives are almost always brine-cured. Finally, check the solution in which the olives are packed. Naturally, if they've been stored in olive oil, they'll have a mellower, olivey taste. Vinegar solutions give a more overt tang, and brine solutions are saltier.
Here are some of the more common varieties, but be aware that the same olive may take different names depending on the store.
Provencal--Usually a black dry-cured olive that is flavored with herbes de Provence.
Sicilian--Usually a large green brine-cured olive that is flavored with red pepper and fennel seeds or oregano.