No, we are neither Protestants nor Roman Catholics. These terms are loaded with significant historical and theological differences that may seem nuanced to most people.
Some know us as Reformed Catholics or Reformed & Catholic. The key knowledge for this is the historical origin. Once you grasp the origin of the doctrines and background of Christianity, which is what Christ has taught and commissioned the Apostles then you will have a better grasp of what we mean by "reformed". Because the word "reform" means reverting or re-forming something to its initial values or plans.
The origin of the term "Protestantns" came from the 1529 “Protestation” at Speyer, when Martin Luther's political supporters (princes) and representatives formally protested against the imperial enforcement of the Edict of Worms (which had condemned Martin Luther).
The core meaning: “Protestant” in the broad sense today refers to any Christian community that broke ecclesial communion with the Bishop of Rome during (or since) the 16th century Western Reformation and rejects Bishop of Rome's (also known as papal) authority. They protested its authority and certain doctrines under the leadership of the Bishop of Rome (e.g. justification, the sacraments, papal primacy).
For us, the Bishops and King in England had long tension with the Bishop of Rome about their doctrines and administration. It was a complex situation. The protests in Germany from Martin Luther catalyzed the whole of Western Europe to voice out against the Church of Rome. In 1534, the Archbishop of England and the King of England finally broke communion with the Church of Rome. Unlike Martin Luther and the others who "protests". For our jurisdiction, we reform the whole nation to revert some of our doctrines and practices to the early Church.
Another way of defining the difference between Protestantism and Reformed Catholic is that Protestants are seen as revolutionists, not reformationists. They protested and revised many doctrines and Church structure into a radical form and direction. Reformed Catholic is not radical or extremist; we did not want to start a revolution. We wanted the Church to be more catholic.
We will not be able to cover the doctrinal differences, but the main points are mentioned above.