That’s not what I mean. There are an awful lot of posts here that refer to “The Church”. Until what people mean when using the term “The Church” is clearly defined for everyone it is difficult for this discussion to have any meaning. That is mostly because everyone does not use the same definition of church. So, what does everyone mean when they use the term Church? I’m certain not everyone uses the Pope’s definition when using the term.
God Bless everyone.
Welcome to the forums. I guess it can be confusing when you are new and we casually use terms as if everyone understands. The answer to your question is that when we say ‘the Church,’ we generally mean the Catholic Church (all rites). But you have to check context and which forum it is posted in. Sometimes it is meant more narrowly (ie only the Latin Rite) and sometimes more broadly.
In this case, we are speaking of the Catholic Church (Latin rite). The site in the OP is a council of organizations that are in disagreement with the Church to various degrees. They are commonly know here as dissident or dissenting Catholic organizations. In most cases, they have remained in the Church organizational structure even if they claim differences with her on matters of doctrine or practice. The was some confusion earlier in the thread because there is a group that is called 'The American Catholic Church in the United States. This is a group that has been created as a split from the Old Catholic Church (in the 1990s) which itself separated from the Catholic Church in the 1870s. Neither the Old Catholics, nor the American Catholic Church in the US have any ties to the Catholic Church since the 1870s.
As I said, context is everything.

You are here in the Traditional Catholicism forum and pretty much everything in this forum is about the Catholic Church - usually Latin rite but other rites are sometimes discussed here. The Pope’s definition of the Church is a very good start to understand what people in this forum mean by Church.
In some of the other forums you will encounter a broader use of church (usually not capitalized) - especially in the Non Catholic and Apologetics forums. Often that definintion includes all Christians and is the general use of the word, which means ‘universal’.
Another question that I have about the “in communion with her” part of the response. Are we talking about being in communion with the catholic faith or do we mean being in communion with Father?
When we use the term “in Communion with** her,**” we mean in communion with the Catholic Church. The Church is usually referred to with the feminine pronoun. This is the Church Jesus founded and is in communion with the Father as Jesus himself was. We are not “Father only” or “Jesus only” as some other faith traditions may be. We are solidly trinitarian.
Again, welcome. I hope this helps.
P.S. I see you are a new Catholic - double welcome. Even after RCIA there is much to learn. You might want to read some of the tracts on the Catholic Answers home page. They give a great overview of Catholic teaching and are a good starting point for questions.