Most of the time when folks say "cleaner shrimp," they are referring to the skunk cleaner shrimp (what the OP had a picture of).
However, there are actually several species of cleaner shrimp including the peppermints, fire shrimp, coral banded and more. The reason they are called cleaner shrimp is that in the wild, they will stake out a small territory where fish will come to have dead skin and parasites removed and even have stuff removed from inside of their mouths. You can probably find photos or videos of them climbing over morays or groupers providing this service. (I seem to remember reading that scientists think the long white antennae send a signal to the fish that signals "don't eat me!") In captivity, the skunk cleaners are the only ones I know that will still do this regularly.