Urbanization is a huge debate in the field of history... Population size is just one factor in many cases for the definition. Monument types (religious buildings, palaces, etc.), administrative functions, population density (particularly in relation to the surrounding rural region), written record, wealth differences, and specialization of crafts. So, depending on how many of these factors a settlement possesses the degree of urbanization for the settlement would change.
However, this just helps in defining urbanism, not exactly classifying town vs city.

That pdf is amazing though and definitely getting added to my inspiration folder.