Are there types of instrument approaches besides precision and non-precision?
All approaches can still be categorized as a precision or non-precision.  Some of the terminology has changed, radar approaches are becoming less common and and GPS approaches are becoming more common, but the fundamentals are the same.  Precision approaches still provide glideslope guidance, and non-precision approaches do not.  

It may be important to note that many flight computers blur the lines some with GPS approaches.  There are approaches where the plate still calls the bottom altitude an 'MDA' (instead of 'DH' or 'DA') as you would in a normal non-precision approach, but the flight computer will generate a custom glide slope to that point.  Because this is generated artificially inside your aircraft and not schematically planned by a certified official, this still only qualifies as non-precision.

All in all, if you're trying to pick up instrument flying after a long break, you'll still be good to go with your basic understanding of precision versus non-precision approaches.