Shells are the outsides without liners I think. Some people like it that way because they can control the layering separately.
your statement is correct but it has nothing to do with softshells.
a shell has no insulation, is very waterproof, is somewhat breathable in the right conditions, windproof.
a softshell often has some light insulation, can be waterproof (more and more are made with goretex/goretex-style laminates) are generally very breathable, and are softer and quieter than a shell, more puncture resistant.
shell: a very waterproof outer layer
softshell: a very breathable outer layer, can be used as a light insulating layer, may be used as a waterproof outer layer.
part of the problem with defining them is that a softshell is kind of an ambiguous term. when they first came out they were all hoodless, insulated, either windstopper or not, and meant for use under a shell or alone during high-aerobic activity.
now softshells have evolved into actual shells, that are soft. so a three layer laminate that is(?) waterproof, very moveable, nearly as light or as light as a hard shell, with no insulation at all.
so part of it could easily be: what kind of softshell are we talking about?