The Mandarin orange, also known as the mandarin or mandarine (both lower-case), is a small citrus tree (Citrus reticulata) with fruit resembling other oranges. Specifically reddish-orange mandarin cultivars can be marketed as tangerines, but this is not a botanical classification. The tangerine (Citrus tangerina) is an orange-colored citrus fruit that is closely related to the mandarin orange (Citrus reticulata). Taxonomically, it may be named as a subspecies or variety of Citrus oculata; further work seems to be required to ascertain its correct scientific name. Tangerines are smaller than common oranges, and are usually easier to peel and to split into segments. The taste is considered less sour, as well as sweeter and stronger, than that of an orange. So,this is what wikipedia says. In fact, people many times use the terms mandarines and tangerines as equivalents.

To be honest, unless they're fruit-growers or chefs, most ordinary people are fairly confused about citrus fruits. We know that oranges are the larger, spherical fruits that don't divide easily into segments, but beyond that, most English-speaking people can be pretty vague about the names. The commonest orange-skinned citrus fruits in the west are tangerines, mandarins, satsumas and clementines, but a lot of people actually wouldn't be able to tell the difference.

There are several types of mandarins. In fact, this is considered an entire class of citrus fruits. So a tangerine is one type of mandarin fruit.