with lever towards left - usual auto box as yu describe.
with lever to right yu are in Sports/Manual mode - ie it revs higher in each gear - its a good way to check the box coz if it dont change nice and smooth its got a problem, usually it changes down then up instead of just up!! - or you can use it as a manual sequential box - nice when yu is hoofing it.
If yu are going to tow with it - get an aftermarket oil cooler for it.