The wrasse family is the second largest family of fishes behind the gobies. So there are a ton of em out there and it can get a lil confusing as the taxonomy is a lil murky in some areas. I think its easier to do this if we talk about this in terms of genus. There are I think 50 maybe 60 or more genuses of wrasses out there but only 6 of those genuses are really worthy of discussion in terms of reef tanks.
Cirrhilabrus, aka fairy wrasses - These guys are all reef safe and generally can all be housed together. They are some of the prettiest of the wrasses available. Some are more aggressive and territorial than others though and results may vary. They don't really pick at the rocks much as they are primarily strict plankitvores. As such they don't actively hunt the rockwork like a lined wrasse or a mandarin. They will eat flatworms though when they see em or bristleworms or any other morsel that catches their eyes. I love watching them eat bristleworms in particular or any piece of large food. They will take the piece of food and scrape it against a favorite scraping rock. This will break the piece of food up enabling them to swallow the bits. I've seen many a fairy grab a big piece of food and then scurry off to their favorite lil scraping rock. It's hilarious. These guys do flash as well which makes them so much fun to watch. When a fairy flashes you downtown its bad and you don't want to see it... but when a fairy wrasse is flashing you man its like the sun just came out from behind the clouds for the first time in forever. Its beautiful regardless of the species.
Parachelinus, aka flasher wrasses - Closely related to the fairy wrasses in body shape and look, they tend to be like smaller cousins. They all tend to look somewhat similar until they flash at which point you will be startled by their transformation at times. These guys are completely reef safe and are very peaceful in general. Keep in mind that even the most peaceful wrasse may be aggressive towards conspecifics as they are somewhat territorial. They get along with faieries just fine in most tanks and can be housed alongside them. They are kinda skiddish though and need to feel secure to start flashing. Like the faieries, these guys rarely pick at the rocks.
Pseudochelinus, lined wrasses - This includes common wrasses like the 6-line, 4-line, mystery, and secretive wrasses. These guys get more and more territorial with age and eventually they will almost without question kill most other wrasses regardless of the size differential. They have a special hatred of faeries and flasher wrasses it seems though and will typically seek those guys out and end them post haste. I have seen them get along with some other wrasse genuses though but this may be a case by case situation as results seem to vary. In general though its best to keep these guys as the only wrasses in the tank. They are proficient at picking over the rocks for life and do so throughout the day but will also eat from the water column without difficulty.
Halichoeres, no common name - This genus gets a lil hazy as some of them seem to be placed their incorrectly. The most common fish in our trade from this genus though include the H. crysus aka yellow coris wrasse, which is more aptly called the canary wrasse and H. iridius aka the radiant wrasse. There are a bunch of other wrasses in this genus too that are in the hobby such as the x-mas wrasse, hoeven's wrasse, and green "coris" wrasse. Many of the members of this genus are commonly not considered "reef safe". They will not harm corals but may nip at snails or hermits. It's my experience though that the smaller members of this genus are very "reef safe" and will leave hermits/snails alone for the most part. They are pretty good at scavenging the rocks and rival the lined wrasses in terms of being good rock scavengers. These guys are in general unaggressive and can be housed with faeries and flashers without a problem.
Coris - Some wrasses from the Halichoeres genus are mislabeled commonly as Coris wrasses. In actuality coris wrasses are quite different and tend to be fairly aggressive and not reef safe. These guys will mow through snails and hermits like candy and can be uber aggressive with other wrasses and fish at times. Beautiful though, but should only be used in FO tanks.
Bodianus, hogfish - These guys are called hogfish because of the rooting behavior of a few of their members. They also look slightly different than wrasses but definitely are types of wrasses. There are a few that are common in the hobby for reef tanks like the two-spot or the peppermint. Some get quite large though and should be FO. Hogfish are pretty similar to lined wrasses in that they are good at scouring the rocks but like them they are also pretty aggressive once they reach maturity. They may kill other wrasses and should not be housed with them. I'm not sure how they would fare with a lined wrasse though...
There are a bunch of other types of wrasses from various genus that I didn't cover as I think these are the major ones, especially the first 4.