There are some good scholarly papers on the TPV/SPV relationship(and correlation to the AO), and its complex to say the least. They are completely separate entities, and sometimes there is little to no interaction(coupling) during winter. The reality is, for sensible weather, we are far more interested in the TPV, which is actually larger(multiple vortices), and directly influences our weather. We want a pattern that can disrupt and dislodge these vortices, and bring them south. That's how we get the cold down into the midlatitudes. It can happen at times even with a relatively strong SPV/+AO, as occurred 2013-14 with the big EPO/WPO block. In general though, when we have a persistently negative AO winter(which we clearly want) the SPV is a weakling, and it gets that way largely by transfer of heat into the upper trop/strat.
eta- @Ralph Wiggum
Good read here: https://journals.ametsoc.org/view/journals/bams/98/1/bams-d-15-00212.1.xml