No, they have not always used those terms. It doesn't seem that long ago that the chapels were referred to as "Mass Centers".
The chapel in Linden, VA is what I would consider a hybrid chapel - half SSPX and half diocesan parish. That is what they are working towards, full integration into the diocesan structure. If the local bishop (Burbidge) wasn't so opposed to the Society I think it would be no different than an indult "parish", and there would be N.O. priests offering the sacraments to the mostly willing "parishioners" when the Society priests needed help. With 90% of the faithful being Summorum Pontificuм induters who bounce back and forth, what difference would it make to them? Those of us who would have a problem with it are a very small minority. It's only a matter of time until the deal with Rome is revealed, and with Francis on his last leg, it may be soon.