No just as tangerines are not oranges nor oranges grapefruits. Lemons grow on lemon trees and while lemons when young do resemble limes, limes grow on lime trees. Oranges, grapefruits, tangerines and citrus in general all resemble limes when young. Citrus trees can however graft themselves to other citrus trees via their root structure and this in the long term will affect the taste of the fruit. My neighbor for instance has a tangerine tree which grafted itself to a lemon tree thus souring the tangerines and making them inedible. All they really do is fall in my yard if I don't trim it back at the fence line and are a real pain to pick-up because there are so many and they are so small. Lol
Limes are a different type of citrus tree. A lime tree produces limes, a lemon tree produces lemons. There are other varieties of citrus, such as tangerines, tangelos, several types of grapefruit and oranges. Interestingly enough, a lot of orange trees are grafted onto lemon tree roots, because they are more hardly and disease resistant. But those produce only oranges.