The pictures you posted are correct on which tooth is which.
Not all mares get canine teeth and of the mares that do get them not all erupt threw the gum line.
Wolf teeth need to be removed. Canine teeth just need trimmed down so that a tall tooth doesn't hinder things such as the bit going in and out of the horses mouth.
The canine teeth are typically erupted by the time the horse is 5 years old. How old is your mare? If she is at that age or older then chances are they'll stay under the gum line. If you aren't 100% sure on what you are seeing then have an equine dentist or a vet evaluate her to make sure that there isn't another issue going on.
Fun fact about canine teeth in mares that my dentist shared... mares with NO canines tend to be the least "mareish", lower on the pecking order and easy to get along with. Mares with one canine are middle of the road and mares with two or more canines tend to be the moody mares, sometimes hard to get into foal, sometimes act studdish/hormone imbalance and top of the pecking order. I wasn't sure if I believed him or not so I told him if that's the truth Jade will have a face full of Canines, Molly, eh, probably none and Zavrina will certainly have none. We checked and sure enough, Jade with hormone imbalances and the b*tchiest personality who happens to be lead mare has 4! Molly has one that hasn't erupted and Zavrina, a very docile, bottom of the pecking order sweetheart has none. She was also very easy to breed. Just thought it was interesting :)