A fighter is now, since 6.0, any military craft of 500 tons or less. It does not need an engine, so you can now build defence sattellites with your fighter factories.
While not classified as fighters for maintainance purposes, commercial designs of 500 tons and less can also be built using fighter factories.
A fighter engine, is simply any engine that will fit into a fighter design, there is no longer a differentiation between fighter engines and ship engines.