Like weapons, there are a great many ships within “Star Wars.” But there is a distinction between classes of ships and specific ship names. Ship classes, such as an X-wing or a TIE fighter, are not capitalized beyond the identifying letters. But a specific class of ship under a given category, such as a TIE Interceptor, for example, would be capitalized. An Imperial Star Destroyer is a specific class of ship, but it is a type of capital cruiser.
Aside from broader classifications, there are ships that have specific names, such as the Millennium Falcon. That is a singular name given to Han Solo’s treasured ship, which is a modified Corellian light freighter. Corellian, in this case, is capitalized because it is in reference to the planet Corellia, but the rest of the ship classification is not.