Typological-classification is determined by comparison of physical characteristics with a type specimen; descriptions provide detailed records of physical characteristics of many organisms, but does not allow for genetic variations.
Biological-classification is determined by similar characteristics and ability to produce fertile offspring; working definition applies in most cases, but some organisms interbreed occasionally. Doesn't account for extinct species.
Phylogenetic-classification is determined by evolutionary history; accounts for extinct species, considers molecular data, and solves problems of other species concepts, but evolutionary histories are not known for all species.
Source: Biology Class