... I think your question answers itself. It's called a SHIPyard for a reason. Factory stations are meant to build anything (items, droids, I also do believe small ships) while shipyards are more specialised (large ships). The larger the shipyard, the larger the ship you can build. Other than that, I'm pretty sure they can't be tooled to build anything but ships.
Factory Stations can build droids. Shipyards cannot.
When in doubt check the
“Factories and factory stations are limited to ships less than 80metres in length. All Boats and Submarines are produced in Naval Shipyard facilities. All medical items are produced in Labs or Medical Factory Stations. All other ships, vehicles, items, weapons and droids are produced in factories or factory stations.