Top Solder is the top (primary component side) solder mask, as you describe, it is the one which is commonly for the green color material (though you can get many different colors). The apertures in it are for exposing the pads, and annular rings on through-hole for soldering.
Top Paste is the layer that defines the paste mask for the top side Surface Mount component pads. The PCB assembly shop would use this to make a stencil for the top side SMT pads.
"Solder mask" and "Paste mask" are just general versions of the above - you will generally have a bottom side solder mask on any through-hole PCB or PCB with vias, or if your PCB has components on both top and bottom sides. Same thing with the paste mask if bottom side SMT components are used.