Saying "no relation" is almost stretching it a bit. I kinda give hats off to someone for the slipup. It's not the same legal entity but there's a continuous ideological (and even personal) connection going all the way back.

The way I see it ... Peter Lougheed through Getty and (arguably Stelmach era) was a bit of a brief interruption. His urban, pragmatic PCs pushed the older rural, evangelical Socreds out of power in the 70s.. but that populist movement just went briefly into a (vaguely) outsider status, organized through Alberta Report, etc got into Klein's cabinet, found a national voice in Preston Manning's Reform Party, and returned provincially via the Wildrose Party, and finally triumphally recaptured the province under the banner of the UCP

So not legally the same part, but frankly just really the same minus all the weird fixation on currencies, banks, and anti-Semitic conspiracy theories (... so far!)

All of this off topic from rats. (Maybe?)