Yup. Same supply source for some routers, and both use BTW. But that's it. In fact, until recently, they both used different products from BTW - with Plusnet using shared WBMC, and BT Retail using dedicated WBMC. And, of course, the ISP's own hardware sits at the far side of the WBMC host links.
Plusnet is moving to a dedicated WBMC network too - but that means they get their own dedicated connectivity ... likely with their own set of congestion issues.
http://forum.kitz.co.uk/index.php?topic=16711.0
So, the only real commonality is the router. And, having read lower, this looks to be the case.