The 32 are two strap standard SPD cleat shoes that you can walk in.
They are a basic road/tourer shoe
RT82 are (quote from road.cc)
Shimano have a new road touring shoe in the shape of the RT82 aimed at sportive riders, tourists, and anyone else who wants that road look without the faff of road pedals and cleats. RT? road touring, see. The RT shoes have the same uppers as Shimano’s road shoes but they come with rubberized soles so you can walk in them. You wouldn’t want to walk too far, mind, because the soles are stiff, but you’re not going to skitter about like a sheep on lino.
The ratcheted strap allows for tighter/snug adjustable fit.
Hope this helps