Right, bi-linear means when you sample a pixel's colour from a texture map, you linearly interpolate it with the adjacent pixels, twice (hence bi-linear). With Tri-linear, it's the same, but you linearly interpolate three times.
Anisotropic Filtering is a different kettle of fish. It's a filtering technique relying on mip-map levels, as the further way from the camera you are, then a lower resolution texture is used. Anisotropic Filtering basically means that more higher resolution textures are used, and I suggest you look at these two images to see the difference (the coloured bands are the mipmap levels)
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