In Swedish, I learned this week, there are two words for mushroom: svamp [svamp] (fungus, mushroom, toadstool, sponge) and champinjon [ɧampɪnˈjuːn] (mushroom) [source].
Svamp comes from the Old Swedish svamper (fungus, mushroom), from Old Norse svampr / svǫppr (sponge, mushroom, ball), from the Proto-Germanic *swammaz / swambaz (sponge, mushroom, fungus, swamp), which is also the root of the English word swamp [source].
The Old English word swamm (mushroom, fungus, sponge), and the Middle English swam (swamp, muddy pool, bog, marsh; fungus, mushroom), come from the same root as well [source].
Mushroom was borrowed from the Anglo-Norman musherum / moscheron (mushroom), from the Old French moisseron (mushroom), possibly from the Old French mosse / moise (moss), from the Frankish *mosa (moss) [source]
Champinjon was borrowed from the French champignon (mushroom, fungus, accelerator), from the Vulgar Latin *campāniolus (grows in the field), from the Late Latin campāneus (pertaining to fields), from Latin campānia (level country), which is also the root of the words campaign and champagne.
Apparently champinjon is used to refer to mushrooms used as food, and was borrowed into Swedish in 1690 [source], while svamp refers to mushrooms and fungi in general.