Tangerines (Citrus tangerina), mandarin oranges (Citrus reticulata), and clementines (Citrus clementina) are each small orange citrus fruits, easily confused with one another. Mandarin oranges are found year-round in cans, jars, or small fruit-packs at the grocery store. Tangerines and clementines are only available seasonally. Clementines are typically seedless; tangerines are not.
A pummelo (pomelo) is a cross between a grapefruit and an orange. The pummelo is usually green, sometimes other colors. A tangelo is a cross between a mandarin orange and either a pomelo or a grapefruit. The Minneola tangelo is a cross between a Duncan grapefruit and a Dancy tangerine. A Honeybell Tangelo is a cross between a Thompson tangerine and a pomelo.
The kumquat looks like a very small orange. They are used to make preserves or marmalades, and are often added to recipes — main courses as well as desserts — for flavor and color. This fruit has few seeds and is sometimes eaten whole, without peeling.
The health benefits of citrus fruit are many. They are good sources of Vitamin C and potassium.
Several different types of citrus are high in carotenoids (beta-carotene and similar compounds). Some carotenoids are used by the body to make vitamin A; lutein and zeaxanthin are necessary for good eye health; all the carotenoids are associated with a reduce risk of different diseases. The six major carotenoids are: alpha-carotene, beta-carotene, beta-cryptoxanthin, lutein, lycopene, zeaxanthin.
Oranges contain beta-cryptoxanthin along with some lutein, zeaxanthin, alpha-carotene, and beta-carotene.
Pink grapefruit is very high in lycopene; other good fruit sources of lycopene are guavas, watermelon, and tomato. Pink grapefruit is also high in beta-carotene. The white variety of grapefruit is low in all carotenoids. Caution: Grapefruit interacts with several different types of medications. See this Drugs.com article: Drug Interactions with Grapefruit Juice
Mandarin oranges are a good sources of beta-cryptoxanthin, lutein, and zeaxanthin; they also contain some beta-carotene.
The citrus fruits are also the main source of a subtype of flavonoid called flavanones (eriodictyol, hesperetin, naringenin). Flavonoids have an anti-inflammatory effect on the body. Recent studies indicate an association between higher flavonoid intake and lower risk of cancer and cardiovascular disease.
Oranges are a good source of the flavonoid hesperetin. Grapefruits are high in the flavonoid naringenin. Lemons are high in eriodictyol; another good source of this flavonoid is peppermint. Tangelos and mandarin oranges are each high in both hesperetin and naringenin.
A 2010 study published in the International Journal of Cancer found that daily citrus consumption decreased the risk of pancreatic cancer by 38% and risk of prostate cancer by 37%. 
A 2007 study published in the American Journal of Clinical Nutrition found that high intake of carotenoids reduced risk of all-cause mortality by 31%. All-cause mortality is all causes of death as a set (usually excluding accidental deaths). 
A 2012 study published in the same journal found that high intake of total flavonoids reduced risk of death from cardiovascular disease by 18%. 
And there are many more studies of this type. Citrus and the carotenoids and flavonoids in citrus fruits are important components of any healthy diet.
 Li et al., Citrus consumption and cancer incidence; International Journal of Cancer. Volume 127, Issue 8, pages 1913–1922, 15 October 2010.
 Agudo et al., Fruit and vegetable intakes, dietary antioxidant nutrients, and total mortality in Spanish adults; American Journal of Clinical Nutrition. June 2007. vol. 85, no. 6, p. 1634-1642;
 McCullough et al., Flavonoid intake and cardiovascular disease mortality in a prospective cohort of US adults; American Journal of Clinical Nutrition. February 2012 vol. 95 no. 2, p. 454-464.