Both the deciduous (or temperate) forests and the boreal forests (taiga) can be found in the temperate zones of the world. Taigas are the largest terrestrial biomes.
Both deciduous forests and boreal forests experience 4 relatively distinct seasons; however, the former experiences a wider temperature range with varied precipitation patterns, while the latter is relatively cold most of the time.
Deciduous or temperate forests consist of deciduous plants and trees, which means that they that shed leaves during autumn and remain inactive during winter (e.g. oak, maple, and ash), while boreal forests mostly consist of evergreen trees, primarily the conifers (e.g. pine, cedar, juniper, and redwood).
The two figures below show the different (geographical or climate) zones, and the different biomes, respectively, found all over the world.
(Figure sources: 1. https://en.wikipedia.org/wiki/Temperate_climate#/media/File:World_map_indicating_tropics_and_subtrop....
2. http://www.bio.miami.edu/ecosummer/lectures/lec_biomes.html)