Are we Roman Catholic? Theologically, yes, we hold to all 20 doctrinal Councils and acknowledge the primacy of Peter (the pope and his valid successors).
Are we the same as the mainstream Catholic down the street governed by a Diocese appointed by Rome. No.
We are distinct from the juridic and administrative structure of Rome as outlined by papal grant of Pope Eugene III in 1245, confirmed by Pope Leo X, and the Fourth Lateran Council. We register our consecrations with Rome, but maintain the rights previously granted to protect the Old Faith and to select our own leadership. From the Vatican’s perspective we are valid but juridically irregular (cf. Dominus Iesus n17 ; Congregatio pro negotiis ecclesiasticis extraordinariis prot no. 1245/83). We acknowledge the Petrine Office and desire eventual juridic regularity with Apostolic See.
Rome says in reference to prelatures/Churches such as ours: “Therefore, there exists a single Church of Christ, which subsists in the Catholic Church, governed by the Successor of Peter and by the Bishops in communion with him. The Churches which, while not existing in perfect communion with the Catholic Church, remain united to her by means of the closest bonds, that is, by apostolic succession and a valid Eucharist, are true particular Churches. Therefore, the Church of Christ is present and operative also in these Churches, even though they lack full communion with the Catholic Church…” 1
According to the New Rite Catholic Canonist John M. Huels, JCD in his fine manual for explaining Canon Law to the active clergy, he explains Canon 844 refers to churches that are irregular but acknowledges that in certain circumstances it is licit to receive Eucharist, Extreme Unction and Penance while being a member of the Catholic of Paul VI’s iteration (Vatican II). If and only if the minister of the sacrament is VALIDLY ordained.
He states “The principal condition is that these sacraments can be received by validly ordained ministers. These are ministers who belong to ‘churches that have preserved the substance of the Eucharistic teaching, the sacraments of orders, and apostolic succession’ (Secretariat For Promoting Christian Unity, Communication, Oct 17th, 1973, AAS 65  616; CLD 8:471, no. 9). This would include ALL Eastern non-Catholic Churches [Orthodox etc], the Polish National Church, Old Catholics and Old Roman Catholics. 2 Note that this situation does not apply to the Anglican Communion.3
“It is imperative to understand that just as the mere claim to be “Catholic” or “Roman Catholic” guarantees nothing about someone’s doctrinal orthodoxy, moral rectitude, or authentic worship; neither does the claim to be an “Old Roman Catholic.” Titles, names, and labels do not insure reality. In today’s world, one has to ask questions and receive reasonable answers. The Old Roman Catholic Church, See of Cær-Glow is not affiliated with those who would bend the moral law, compromise with falsehood, or offer false and distorted worship to Almighty God. Under God’s law there can be no “gay marriage,” no ordination of women, no “clown Masses,” no Marxism, no Modernism, or anything else that has not come down to us from ‘the Father of lights, with whom there is no change, nor shadow of alteration.‘”4
“It embraces all such doctrine of the Apostolic See of Rome, and it condemns all heresies and other errors condemned by that same See. It accepts as Catholics those who share this doctrine and conduct their affairs accordingly.” (Constitution of the Old Roman Catholic Church, Article II)
1 Congregation for the Doctrine of the Faith, DECLARATION DOMINUS IESU: On the Unicity and Salvific Universality of Jesus Christ and the Church., n.17.
2 Huels, J.M.,The Pastoral Companion: A Canon Law handbook for Catholic Ministry, 3ed. Franciscan Press: Quincy University), p335.
3 Ibid. p.337.