"know that when ordinary people like me say "Scots English" they mean all sorts of things running the gamut from English laden with Scots words to strictly Scottish English,"

I don't think Jack was meaning to be pedantic or pernickity. He maybe could have put it better but he was just pointing out that the term Scots English, Scottish English or probably more properly Scottish Standard English (whatever one wants to call it) is not the same thing as the Scots language. SSE is simply standard English as it is spoken in Scotland. Basically accent aside just the same as standard English but with Scotticisms like pinkie, thrice and gotten - plus some of the more commonly known Scots words - though even they are often used just for comic effect and wee asides. Scots itself though closely related has different vocab, different spelling, different grammar etc. Many people of course speak a mix-max though others change between the two with ease depending on who they are speaking too.

Though there has never been a census count govt estimates put the number of actual Scots speakers at about 1.5 million - whereas just about everyone can speak SSE. Some better than others no doubt :-)