Oranges and lemons are the most commonly consumed citrus fruits, but the citrus family is a lot more complicated than that. There are four fruits from which most of the rest of the citrus family originate: the mandarin, the pomelo, the citron and the papeda.
The mandarin (Citrus reticulata) is a small citrus fruit, and the only citrus that produces sweet fruit. Both the sweet orange (Citrus × sinensis, what you and I would simply call “an orange”) and the sour or marmalade orange (Citrus × aurantium) are crosses between the mandarin and the pomelo (Citrus maxima), and thus it would be more correct to refer to oranges as large mandarins rather than mandarins as small oranges.
The satsuma (Citrus unshiu), tangerine (Citrus tangerina) and clementine (Citrus × clementina) are all cultivars of the mandarin, and if the tangerine is crossed with the pomelo this yields the tangelo (Citrus × tangelo).
The pomelo is a large, thick-skinned citrus fruit. As explained above, the sweet orange is a cross between the pomelo and the mandarin, and if the sweet orange is crossed with a pomelo this yields the grapefruit (Citrus × paradisi). If the pomelo is crossed with the citron (Citrus medica) this yields the lemon (Citrus × limon)).
The citron has a similarly thick skin to the pomelo. It is crossed with the pomelo to yield the lemon, and the lemon again with the pomelo and mandarin to create the rangpur (Citrus × limonia). It is also crossed with the papeda (Citrus subg. papeda) to yield the lime (Citrus × latifolia and others). (The key lime (Citrus aurantiifolia) is a separate species, like the kumquat (Citrus japonica), that does not originate from the four “fathers” of the citrus family.)
The papeda is a subgenus of citrus that contains a number of fruits. As mentioned above, a cross between the papeda and the citron yields the lime, and the yuzu (Citrus ichangensis × Citrus reticulata) is the result of a cross between the papeda and the mandarin.
Disclaimer: I did try to sum up this post in a diagram, but I gave up in the end.