I have been think about this for a while.  The difference between air fighters/bombers and space fighters/bombers

are as follows.

Air fighters/bombers

Air fighters are built to support ground troops and take out other fighters and bombers.

Air bombers are built to take out factories and other stragic targets.

Exceptions  Carrier fighters are designed to attack ships at sea.

The usa airforce has designed a bomber(although I think the current one is a transport plane.) to be able to take out a destroyer with a single shot.

Space fighters/bombers. 

Space fighters will be designed to take out other fighters and space bombers.

Space bombers will be designed to take out spaceships under way(small ships in a single shot), and space bases and other stragtigic targets.

Exceptions  Space fighters with enough support will also be able to take out spaceships.  Both should be able to be used as plantery bombers.

Space bombers may also be known as heavy fighters.