Yes. Stainless steel will form oxides. A good etching primer can neutralize them. Primers also smooth the surface and provide a better surface for the paint above it.
The two you show are different. The one for auto finish has more solids and builds up thicker for wet sanding to get a perfectly level finish using a sanding block. Filling low areas with a high solids primer and then blocking get the surface free of waves and imperfections. That's the first step to get that perfect show car smooth finish down a body line. Although, I don't recommend rattle can primer for that.
As far as rattle can times, I let the primer dry for an hour or so then top coat it. All should be sprayed wet (aka, should look wet as you cover more area) to prevent dry rough spots where it will not adhere as well. Then let top coat dry very thoroughly before handling. A day or so is my rule unless I'm in a hurry.
Fwiw, I wouldn't use the top one either. I prefer good etching primers to get a better bond. That bond is the base for your finish. A good blasting and cleaning with a solvent such as acetone leave a clean finish with a good base for the mechanical bond also.