Here is a wikipedia article about antistopic rendering. I think the main idea is that in mip-mapping high frequency signals are filtered out from multiple dimensions, but under projections, the filtering is done taking into account many relative coordinate size ratios.
So it seems like anisotropic is essentially a uniform filter on an entire texture space, whereas isotropic filtering is a function of the distance / size of the texture space relative to the screen space. In other words, bilinear filtering is anisotropic because it doesn't interpolate between different mip levels, while trilinear is isotropic because it blurs a texture more when it's smaller relative to the screen size.
Isotropic filtering means that the filters extent (the red box drawn in this figure, a.k.a. the area integrated over by the resampling scheme) has the same extent in the u and v directions. More generally, if the filter was a circle instead of a box, an isotropic filter would be radially symmetric in all directions. Anisotropic filtering means that the extend of the filter is different in different directions. For example, in this example, an anisotropic filter would much better approximate the true region (green region) that needs to be integrated to obtain the properly filtered value of the texture.