Question: What is the "parish" Church?

Answer from the Catechism para. 832:

The Church of Christ is really present in all legitimately organized local groups of the faithful, which, in so far as they are united to their pastors, are also quite appropriately called Churches in the New Testament.... In them the faithful are gathered together through the preaching of the Gospel of Christ, and the mystery of the Lord's Supper is celebrated.

Question: How does the parish church connect to the universal church?

Answer from the Catechism para. 1396:

The Eucharist makes the Church. Those who receive the Eucharist are united more closely to Christ. Through it Christ unites them to all the faithful in one body -- the Church.