If they are not the same, then what is the difference? Please help me out here.
Yes, tannins are pigments but they aren't really the main plant pigment. Plant pigments usually refer to photosynthetic pigments (chlorophyll, carotenoids, etc.). These photosynthetic pigments give the leaves their green color (or yellow/orange in the fall). Tannins are non-photosynthetic phytochemical (involved in plant metabolism and internal functioning), but they are also a pigment. Tannins (and lignins) are brown. This is was gives dead leaves and wood their color. Tannins also leach out of the leaves when soaked in water (same process as brewing a cup of tea). So tannins are pigments when they leach out of leaves and stain water (or other things) brown, but they are not photosynthetic plant pigments. In other words, it depends on what context you are calling a tannin a pigment. In a live plant they are not a pigment (judgment call here). In a dead leaf or when they leach out of a leaf they are a pigment.
