Ships and templates are available in the game you define them in AND in games that you start after a ship or template has been defined.
This means that if you have an active game and you start a different game to design a new ship, that design will not show up when you reload the first game.
It is not just the ship and template files that behave this way, but all game resources (like the XML files). This is purposely made so that the required data is always in the game save file. This allows you to transfer the game save to another machine (or SD support) without also having to transfer all support files. Also it prevents cross incompatibilities between the game data and the support files.
The disadvantage is if you make any changes to xml files, ship designs, mods, etc then you need to start a new game to use them.
So this is working as intended/designed.
Hopes this explains the issue.