The ships with a blue background are your own ships. Ships with a gray background are ships that have been authorized. Ships with a green "Active" banner are currently on a sailing voyage or are moored in the port.
You can mark ships in the list as a favorite by clicking on the heart so that it turns completely blue.
You can also designate one of your favorites as a top favorite. To do so, click on the star so that it turns completely yellow.
You can also manually order your list by pressing ‘…’ at the top bar and then on ‘sort’.The top favorite is always shown first in the list.