Below are the categories Starships normally fall under:
Starfighter- A starfighter was a small, maneuverable spacecraft designed for military combat. The majority of starfighters were piloted directly by living beings, although some were either controlled remotely or by artificial intelligence. These light craft were designed to carry out attacks on sensitive installations and targets that required immense precision.
In fleet battle, starfighters worked in concert with capital ships, harassing warships and striking once their shields weakened, failed or were re-aligned due to enemy capital ship-fire. Alone, fighters had little to no chance of penetrating the shields of capital ships, but most starfighters worked in squadrons and carried weapons like proton torpedoes and concussion missiles. These squadrons could take out a large capital ship with precision fire.
Transport- A transport was a small or medium sized spacecraft or other such craft commonly used for short cargo (or smuggling) runs that didn't require the use of a bulky freighter. Usually equipped with a hyperdrive, though this was not always the case, transports came in a wide variety of sizes and specifications and were produced by a large number of companies.
This class of spacecraft was very easy to modify and adapt, and as such was popular amongst smugglers and pirates. Although most transports were owned and operated by civilians and the criminal element, some militaries used them for the movement of troops and/or their equipment, such as the Sentinel-class landing craft, by Cygnus Spaceworks, used by the Imperial Navy to swiftly deploy its personnel to planets below.
Capital Ship- Capital ship was a general term that referred to any armed military starship that had a length greater than one hundred meters. Ships of this class ranged from small and nimble corvettes to titanic Star Dreadnaughts. The "Mother Ship" would be labeled a Capital Ship, along with other commanding modules, ect.
Space Station- Space stations were artificial structures built for use in orbit or deep space. The term was also used by one standard ship classification system to classify some of the largest and most heavily armed capital ships in the known galaxy.