In the civil world, there are 'licences' (PPL, CPL, ATPL) which contain 'class ratings' and/or 'type ratings', e.g. Single Engine Piston Class, Single Engine Turbine Class, Multi Engine Piston Class, Touring Motor Glider Class, Airbus A320 Type Rating etc etc.
When you first apply for a licence, you also apply for the rating for which you were tested. Thus most people apply for a PPL with SEP Class Rating after taking the PPL Skill Test; thanks to Eurocracy the PPL lasts for 5 years until it has to be re-issued and the SEP Class Rating lasts for 2 years unless revalidated.
A Single Engine Piston Class Rating taken on a PA28 does not limit you to just PA28s as it is a generic rating; conversion training is recommended but not legally mandatory if you then wanted to fly, say, a Cessna 152. No additional licensing paperwork would be needed though.
However, if you wanted to fly a SEP Class a/c with a VP prop, retractable u/c, supercharged or turbocharged engine, tailwheel or cabin pressurisation, conversion training (unspecified) is mandatory and the Flight Instructor or Class Rating Instructor carrying out the training must sign your logbook to confirm that the training had been completed.
If later you wish to add light twins to your licence, after completing the relevant training you take a Multi-Engine Piston Class Rating Skill Test with an authorised Flight Examiner or Class Rating Examiner.
To fly at night, you need a Night Qualification; for military FW pilots this is normally a paperwork exercise if you are 'night current' in military terms. You can also add a UK national IMC Rating to your licence fairly easily if you have a current military FW Green IR, however, you can only use its privileges in UK airspace.