What is the difference between Anglo-Catholicism and Catholicism? I read about Anglo-Catholicism and what I found is that there aren't differences between them and Catholic (in term of doctrine).
Am I wrong?

If I'm not in wrong, the only difference is in the Pope's authority vs the authority of the Archbishop of Canterbury (or the Queen of England), so why they do not come together?

I can't understand the schism.
Granmirupa, in fact you are wrong. There remain considerable differences between most who consider themselves "Anglo-catholic" and those who self identify as Catholic, other than whether the Archbishop of Canterbury, or the Bishop of Rome exercises authority over the church. One of the differences between [Roman] Catholics and Anglo-catholics is that it's much easier to define who is a Roman Catholic. Simply put, a Roman Catholic is a person who accepts the authority of the Bishop of Rome, and accepts the correctness of those doctrines and dogmas, like the doctrine of transubstantiation, the Assumption of the Mother of God, the doctrine of purgatory, and the church's rules regarding the celibacy of the Clergy, and the existence of seven sacraments, that the Catholic church demands that the faithful believe. 

An Anglo-Catholic, especially in the present times, is a much more nebulous identification. The present use of the term dates only as far back as the last 3/4 or 1/2 of the nineteenth century, when certain Divines in the Church of England began to reconsider, and recover some of the customs and ceremonial of the Roman Catholic Church, and began to develop greater appreciation for some parts of Roman Catholic theology. Some of these individuals, including John Cardinal Newman and Henry Manning, joined the Catholic Church, but others, like John Keble and Edward Pusey continued in the Anglican Communion, and continued to subscribe to the thirty nine articles, which rejected the doctrines of transubstantiation, and purgatory, denied the supremacy of the pope, the necessity of unmarried clergy, held that there were two, and not seven, sacraments, and denied that the Apocrypha (deutero-canonicals) were to be included in the Canon of Holy Writ. Also, at the time of the origin of the Anglo-catholic movement, the Roman church still insisted that all liturgy be in Latin, while the 39 articles required that Anglican liturgies be in a language that the people could uncerstand. The result was a series of volumes such as the Anglican Missal, which incorporated most of the form and structure of the Mass, but in English, and with some additions to the prayer of consecration in the English prayer book. During this period, Briggs and Frere produced a psalter which helped re-introduce plainsong tunes (using Sarum, rather than Latin rite endings) for singing the Psalter, and other canticles. And while Anglo-catholics recovered some of the practices relating to rites that the Roman Church considered sacraments, like extreme unction, confessions, and holy orders, the understanding of these rites was never changed so that they were considered sacraments; article 25 (of the thirty nine), still explicitly is the official position of Anglicans, that 


  There are two sacraments ordained of Christ our Lord in the Gospel, that is to say, Baptism, and the Supper of the Lord
  Those five commonly called sacraments, that is to say, Confirmation, Penance, Orders, Matrimony, and extreme Unction, are not to be counted for sacraments of the Gospel...


Anglo-catholiism was never universal in any branch of Anglicanism. In most dioceses, there might be a number of Anglo-Catholic Parishes (sometimes only one or two), while most of the rest of the parishes and missions in the dioceses were Anglican (or in the US, Episcopalian), at the same time as in other dioceses, there might be a larger proportion of Anglo-catholics, and a smaller number of those who were not.

More recent events have cast made the situation even more confusing. There are a small number of Anglo-catholic parishes which are socially progressive, so that they support the Ordination of Women to the clergy, and perhaps other recent social movements. A number of others who self-identify as "Antlo-Catholic" have rejected some of these recent developments, and have joined one of the "continuing" groups. Further, some in the Anglo-catholic movement have come to hold views more aligned to the Roman Catholic church in areas such as the doctrine of purgatory, and some of the more recent Marian developments (e.g., the dogma of the Immaculate conception of the Mother of God), though this is not the official position of any Anglo-catholic group of which I am aware [Note: I am not meaning to represent that there are no Anglo-catholics who hold these view; I'm just not aware of them.]

As to the recent developments of the Anglican personal ordiariate, note that this affects only customs and ceremonies of the liturgy. Presumably, those choosing to take advantage of the terms of Benedict's ordinariate, are still required to adopt the doctrines to which the Catholic Church demands all adherents of the western rite subscribe, such as transubstantiation, and the supremacy of the Bishop of Rome.

So the reasons Anglo-catholics (or at least the Anglo-catholic authoring this answer) do not come together with those who profess the supremacy of the Bishop of Rome, is that there are several areas where there is great difference of opinion about matters of the Faith and the Church. I would also note that since the changes in Roman Catholic theology that have occurred since World War II, (used, not because I mean to suggest that war had much to do with the changes in theology itself, but mainly because it provides a convenient marker for the period of time), and especially since the second Vatican council, do seem to make the differences between Anglo-catholics on the one hand, and Catholics, on the other, at least seem less than they once did.