I don’t know why this is a difficult question. The “Catholic Church” referred to by the ECFs is the same Church with the name today.
The Catholic Church was a clear, visible “institution” from which one could be “expelled” if they advanced heretical beliefs:
“For it is evident that those men lived not so long ago,–in the reign of Antoninus for the most part,–and that they at first were believers in the doctrine of the Catholic Church, in the church of Rome under the episcopate of the blessed (Pope) Eleutherus, until on account of their ever restless curiosity, with which they even infected the brethren, they were more than once expelled.” *Tertullian, On the Prescription Against Heretics, 22,30 (A.D. 200). *
“See that ye all follow the bishop, even as Christ Jesus does the Father, and the presbytery as ye would the apostles. Do ye also reverence the deacons, as those that carry out the appointment of God. Let no man do anything connected with the Church without the bishop. Let that be deemed a proper Eucharist, which is [administered] either by the bishop, or by one to whom he has entrusted it. Wherever the bishop shall appear, there let the multitude also be; by the bishop, or by one to whom he has entrusted it. Wherever the bishop shall appear, there let the multitude also be; even as, wherever Jesus Christ is, there is the Catholic Church.” *Ignatius of Antioch, Epistle to the Smyrneans, 8:2 (c. A.D. 110). *
Notice in the above passage, the Eucharist is not symbolic and thus, can only be consecrated by a bishop or a priest ordained by a bishop.
”Whence you ought to know that the bishop is in the Church, and the Church in the bishop; and if any one be not with the bishop, that he is not in the Church, and that those flatter themselves in vain who creep in, not having peace with God’s priests, and think that they communicate secretly with some; while the Church, which is Catholic and one, is not cut nor divided, but is indeed connected and bound together by the cement of priests who cohere with one another.” *Cyprian, To Florentius, Epistle 66/67 (A.D. 254). *
You are either in union with the visible, Catholic Church or you are not in His Church.
“Concerning those who call themselves Cathari, if they come over to the Catholic and Apostolic Church, the great and holy Synod decrees that they who are ordained shall continue as they are in the clergy. But it is before all things necessary that they should profess in writing that they will observe and follow the dogmas of the Catholic and Apostolic Church; in particular that they will communicate with persons who have been twice married, and with those who having lapsed in persecution have had a period [of penance] laid upon them, and a time [of restoration] fixed so that in all things they will follow** the dogmas of the Catholic Church…”** *Council of Nicaea I (A.D. 325). *
Follow dogmas of the Catholic Church? Where is Sola Scriptura?
“For in the Catholic Church, not to speak of the purest wisdom, to the knowledge of which a few spiritual, men attain in this life…–not to speak of this wisdom, which you do not believe to be in the Catholic Church, there are many other things which most justly keep me in her bosom. The consent of peoples and nations…so does her authority…the succession of priests…[a]nd so, lastly, does** the name itself of Catholic**, which, not without reason, amid so many heresies, the Church has thus retained; so that, though all heretics wish to be called Catholics, yet when a stranger asks where the Catholic Church meets, no heretic will venture to point to his own chapel or house. (INTERJECTION: IS THIS NOT TRUE EVEN TODAY? THE PROTESTANTS ON THIS FORUM SAY THEY TOO ARE CATHOLIC, YET THEY WOULD NOT DARE POINT OUT THEIR OWN CHURCHES IF SOMEONE SHOULD ASK WHERE THE CATHOLIC CHURCH MEETS) such then in number and importance are the precious ties belonging to the Christian name which keep a believer in the Catholic Church…Now if the truth is so clearly proved as to leave no possibility of doubt, it must be set before all the things that keep me in the Catholic Church…For my part, I should not believe the gospel except as moved by the authority of the Catholic Church…for it was through the Catholics that I got my faith in it; and so, whatever you bring from the gospel will no longer have any weight with me. Wherefore, if no clear proof of the apostleship of Manichaeus is found in the gospel, I will believe the Catholics rather than you.” Augustine, Against the Epistle of Manichaeus, 4:5,5:6 (A.D 397)
It was throught the authority of the Catholic Church that St. Augustine got his faith in the gospel. Protestants who believe St. Augustine is Protestant, please take note!