Yes, those are the ecclesial offices, but they are not the only offices recognized by the Church. You can search the catechism online to find others.
Note that these three succeed from the apostles according to the Catechism
1536 Holy Orders is the sacrament through which the mission entrusted by Christ to his apostles continues to be exercised in the Church until the end of time: thus it is the sacrament of apostolic ministry. It includes three degrees: episcopate, presbyterate, and diaconate.
Apostles were higher than the three ecclesial offices because these offices got their authority from the apostles.
Beyond this, I will not disagree, because I think I understand what you are saying.
Matthias was neither selected by Christ nor sent by Christ. Therefore he was not one of Christ’s Apostles which are otherwise known as “The Twelve”. He was, however, a missionary as were the other apostles. Paul was the replacement for Judas as the Twelfth Apostle as he was called by and sent by Christ. Judas was never sent. Furthermore in his call to find a replacement for Judas, Peter quotes two OT psalms, one of which says “…let another take his office” The Greek word for ‘office’ there is episkope, meaning overseer and is the very same word that is translated elsewhere as ‘bishop’. So Peter is calling for someone to replace Judas, not as an Apostle (one of the Twelve) but rather to replace him in the office of bishop that Judas forfeited.
I hear this often from Protestants, and it is incorrect. On the day of Pentecost, there were about 120 believers gathered together in the Upper Room when the Spirit descended upon them all. The people of Jerusalem wondered what all the noise was about, and “Peter stood up with the Eleven.” (cf. Acts 2:14)
IOW, 12 men stood up to witness to the crowds: Peter and “the Eleven” - not “the Ten”. Judas Iscariot was dead; Matthias had filled his office as one of the Eleven. In total, there were Twelve apostles, and this is consistent with the election of Matthias as recorded in Acts 1:
26 Then they cast lots, and the lot fell to Matthias; so he was added to the eleven apostles.
Matthias became one of the Twelve.
Why not? If the Apostles could create other Apostles as you claim with Matthias succeeding Judas then a scriptural precedent is established and so another Apostle should succeed Peter. But as I pointed out above Scripture says that Matthias was only selected to fulfill the office of bishop that Judas vacated. That is why there are no more Apostles.
Because the requirements for being an apostle were that the individual had to have “seen Jesus”.
21 Therefore it is necessary to choose one of the men who have been with us the whole time the Lord Jesus was living among us, 22 beginning from John’s baptism to the time when Jesus was taken up from us. For one of these must become a witness with us of his resurrection.”
So, Matthias, Paul and Barnabas are “Tier 1” Apostles. You can read more about this from a Catholic Answers article here.
I agree and they started with Matthias. Matthias sets the biblical precedent for the Apostolic Succession of Bishops. If he were an Apostle then he would set the biblical precedent for the Apostolic Succession of Apostles which no one claims occurred. Matthias is a bishop, no more no less.
Shown to be erroneous above. Especially in the article. Please read it.