Hi,
Solder mask, stop mask: is needed during PCB manufacturing process. They define the openings in the outer PCB laqueur layer. This laqueur gives the main color to the finished PCB. Often green, but nowadays you can get different colors. Below this laqueur layer there is the copper layer. So when tge solder mask is "open" you have access to the copper for soldering, SMD as well as THM soldering. Here you can see the bare metal, covered with tin (silver shining) or maybe gold covered.
Non "soldering" exceptions: edge connectors. They don't get soldered, but obviously they need an opening at the laqueur layer, so you have acces to the pads for connection.
Copper traces are usually covered by the (green) laqueur. The laqueur layer is isolating (not in the meaning of safety isolation)
Solder paste, paste mask: is what you need to make the stencil to apply the SMD solder paste onto the PCB. Usually only SMD solder pads.
Klaus