1) Tundra is a region with latitudes around and beyond the polar circles (63° 33'). It is characterized by its icy subsoil, high tree vegetation or, in any case, natural trees, which is due to the low heliophany and to the stress of glacial cold. Soils are covered with mosses and lichens, are swampy, with peat bogs in many places. It extends mainly through the north hemisphere: in Siberia, Alaska, northern Canada, southern Greenland and the Arctic coast of Europe.
2) Taiga is a biome with latitude medium and high of the northern hemisphere (from 55 ° N to arctic circle N) characterized by its coniferous forest formations, being the largest forest mass on the planet. Geographically, it is located in north of Russia and Siberia, north of Europe, the Hudson Bay region, north of Canada and the state of Alaska. It is limited to the south by the steppe and to the north by the tundra.
this answer is based on the article The World's Biomes available in: http://www.ucmp.berkeley.edu/glossary/gloss5/biome/