But here's the kicker, no such style ever existed in Scotland. The Americans made it up.
Beer simply wasn't brewed with peated malt in Scotland. The history of Scottish brewing does have some differences with how us English did it, but on the whole they were brewing strong hoppy pale ales to compete with the hoppy Burton Ales (the forerunner of IPA) around the same time as everybody else was, and there is little evidence to suggest they hopped their beers significantly less, or that they ever used peat fire dried malt in brewing beer (only for whiskey).
You could argue that Scottish heavies (or Wee Heavies) are similar to what the Americans call Scotch Ale, but again these contain no peated malt.
The thing is though that the Scotch Ale style (and it is a style, even if a completely modern invention) has been around for long enough in the US now that some people think of it as a true historical style - The same way some people think Tikka Massala is from India, not Birmingham...
The Old Chub Scotch Ale I tried has all the characteristics the yanks like; heavy and sweet, with a big crystal malt aroma and loads of caramel and toffee. The flavour also has the whiskey tinged peat malt character that's expected, plus digestive biscuit and loads of brown sugar.
It's very, 'to style', even if they made it up.
But does that matter?
Jeff Alworth makes a very strong case on Beervana that though the Scotch Ale style may have been born out of ignorance, it is not without worth, if only as an important part of the American craft beer revolution.