How do star card upgrades apply to different varieties of the same vehicle?

The cards will automatically update themselves to affect the ship that you're using.

Your example ("Bomber Weapon Systems") will affect "Ion Cannon Active Time" when you're using a Y-Wing (like your screenshot shows).

If you're using a TIE Bomber or a Hyena-Class Bomber, the exact same card will show that it affects "Missile Barrage Damage".