Original author here and it's been a while since I have read such word salad nonsense, sorry. Why people who have no idea or expertise comment on articles?
GenerateMips API constructs a mip chain by using box/bilinear (equivalent for factors of two) log N times.
Trilinear interpolates across three dimensions, such as 3D textures or mip chains. It is not a method for downsampling, but a method for filtering that interpolates two bilinear results, such as two bilinear filters of mip levels that were generated with "some" downsampling filter (which can be anything from box to Lanczos).
Anisotropic is a hybrid between trilinear across a smaller interpolation axis under perspective projection of a 3D asset and multiple taps along the longer axis. (More expensive)
Trilinear interpolates across three dimensions, such as 3D textures or mip chains. It is not a method for downsampling, but a method for filtering that interpolates two bilinear results, such as two bilinear filters of mip levels that were generated with "some" downsampling filter (which can be anything from box to Lanczos).
Anisotropic is a hybrid between trilinear across a smaller interpolation axis under perspective projection of a 3D asset and multiple taps along the longer axis. (More expensive)