SEP & TMG are type ratings that can be added to the PPL(A); whatever type you do your training & test in will be the type that comes with your PPL(A). The chances are that you hold an EASA PPL(A) with an SEP(land) type rating - check p4 of the EASA licence.
You need the appropriate type rating to be PIC. If you hold an SEP & TMG type rating the hours in both can be combined for the purposes of rating revalidation by experience; if you revalidate by test a proficiency check in either revalidates both type ratings.
To add a type rating, FCL.725 applies, so a course at an ATO (effectively differences training) followed by a skills test.
SLMG was a CAA term. As far as EASA are concerned, a TMG has a non-retractable engine & propellor. If the engine & prop fold away it's a sailplane & you need a sailplane licence to fly it & a self-launch endorsement to take off using the engine.