Why are there many different approach lighting systems?
The different systems generally have to do with ILS landings and the ability to have the runway in sight. As approach systems have gotten better and our understanding of flight mechanics and general operations has increased the need for different systems has evolved. As new requirements come out and new (generally lower) minimums are allowed different lighting requirements may accompany that but not all airports can always afford to install new lighting (and other related things) as such most regulations allow older systems to stay in place so long as the minimums remain. 

In some cases airports simply don't have the physical land at the runway threshold to install larger/longer light systems. In some cases they need to do things like extend out into the ocean to install the lights.