sppx does the same thing, but they are not parishes, either.
parish, parishoner, and pastor imply jurisdictional authority.
Yes. If there is a private chapel in a private home or the rectory, etc., it is called a chapel, and NOT a church. Word will be quietly passed on regarding Mass, etc.
Otherwise, if Mass is for everyone, it will specify Church, in the bulletin or notifications, and an event will be called "Parish picnic, or Church picnic," Parish potluck, Church potluck," etc.
The only other time I have seen chapel listed is if it is an actual chapel within a church where Mass is being said. Larger churches and cathedrals and basilicas, etc., come readily to mind, and those are not necessarily SSPX or FSSP Mass centres, either, but merely referring to the physical churches that are built with one or more chapels in them. Europe is filled with such places. (Then you get into things like crypt churches, too).
Smaller chapels that I have come across in both Diocesan Parishes and SSPX or FSSP Mass Centres or Churches/Parishes are usually dedicated Adoration Chapels, but Mass is sometimes said there, also.
If people want to call their parish or church a chapel, I don't really care. I know what they mean. They are going to a physical building for Mass or the Sacraments. :-)