According to canon:
The starport of a Third Imperium is an area under the control of the Starport Authority. Imperial law applies; local law does not. A starport can be a highport, a downport, or both. A highport can be a single modular cutter module or a giant space station. A downport can be a flat patch of rock or concrete or a giant city within the extraterratoriality line. But the defining characteristic of a starport is that it is the space or spaces that are under Imperial Starport Authority control.
A startown is a place adjacent to a starport that us under local law. It can be a separately managed wing of a space station that also includes a starport, or a village or giant metropolis adjacent to or surrounding a downport. By definition, they are not part of the starport.
A spaceport is a highport or downport other than the primary starport. It can be an annex to the starport, under Starport Authority control, a facility run by the planetary government or a national government of a balkanized world, a facility run by a local government, a private facility, or some kind of jointly operated facility. Although canon doesn't directly say so, it's reasonable to interpret it as saying that a starport is a specific type of spaceport.
That covers canon.
Extrapolating from canon examples and practical reasoning, both startowns and spaceports will have a lot of variation. Spaceports, due to their variety of management possibilities, will obviously vary widely, depending on their ownership and local peculiarities. Startowns may be nothing more than the portion of the local world nearest the starport, but many worlds may have special local laws for the startown, such as free trade zones, enterprise zones, relaxed (or constricted) laws, differing rules for locals and foreigners, etc. On balkanized worlds, a startown might be a district under cooperative administration, with laws that are different from those of any of the world's nations.
Canon doesn't have a term for the regions around a spaceport that is not a starport. But it's reasonable to assume that a spaceport that is not a starport has an associated spacetown.