With regard to the “faith community” designation for Catholic churches, I talked to my priest about this briefly. We recently fully amalgamated three churches into one, closing all three parishes and forming a new one. For a while we were a " faith community" but it was only temporary, we are now a parish. I didn’t exactly understand why. Not sure if this applies to all RC but in our case it had something to do with this transition process and not because of it sounding more inclusive (thankfully!)
Parish is a word with a very definite meaning:
An ecclesiastical society, usually not bounded by
territorial limits, but composed of those persons who choose to unite under the charge of a particular priest, clergyman, or minister; also loosely, the territory in which the members of a congregation live.
Or as it more specifically means in Catholic circles:
the local subdivision of a diocese committed to one pastor.
Faith community and the first definition mean basically the same thing.
However, within Catholic circles, congregations that worship under a priest who is part of a non-diocesan order probably isn’t a parish if the ownership and administration is outside normal Canon Law for parishes. My rationale is that while the worshippers are subject to the Bishop, the Priest isn’t (granted he and his order is allowed to be in the diocese at the pleasure of the Bishop).
Additionally, college newman centers are not parishes. Worshippers are officially members of their home parish. In this case, while it appears to be a parish, it is not one organizationally and under Canon Law. They aren’t required to have Finance Councils as are parishes.
IMHO, this is not a big deal for a parish to refer to itself as a faith community. Parish implies organization, money, buildings, etc. If these have been subjects that in the past were divisive, a change in “name” might allow everyone to start over. This being said, there is no excuse or rationalize not having the name of the parish/faith community designated clearly as Catholic.
And in some cases might be a positive as in Lil M’s example above. I can imagine it useful also in situations where the parish has a particular ministry that transcends boundaries as in one located to serve the poor or a particular segment of society (i.e. the deaf).