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"...both the Orthodox and Catholics have the same criteria for divorce."

On the contrary, the Catholic Church holds that a sacramentally valid marriage is indissoluble. This does not mean that a validly married couple cannot get a civil divorce (civil divorce in itself has nothing whatever to do with a sacrament); but it does mean that, even if a civil divorce is obtained, the validly married husband and wife are still married in the eyes of God, and cannot remarry until the other partner dies.

Annulment is a different matter: it is not divorce. It is based on an investigation of the validity of the sacrament and the vows. If both the husband and the wife made sincere vows (they weren't drunk, crazy, immature, coerced, mentally handicapped, ignorant of the meaning and obligations of the married state, etc.) and were truly free to marry (there was no question of incest, bigamy, etc.), the bond stands; but if the vow was null (defective) from the git-go, there was no indissoluble bond. Hence annulment: a finding of no marriage.

Please direct me to some link if I'm wrong about this. I'm here to learn.

I would be truly grateful to be corrected on this subject, but my understanding is that the Orthodox Church under some circumstances permits divorce and remarriage, even if the couple was validly married in the beginning. That's what my divorced/remarried Orthodox friends tell me.

The church will permit up to, but not more than, three marriages for any Orthodox Christian. If both partners are entering a second or third marriage, another form of the marriage ceremony is conducted, much more subdued and penitential in character. Marriages end either through the death of one of the partners or through ecclesiastical recognition of divorce. The Church grants "ecclesiastical divorces" on the basis of the exception given by Christ to his general prohibition of the practice. The Church has frequently deplored the rise of divorce and generally sees divorce as a tragic failure. Yet, the Orthodox Church also recognizes that sometimes the spiritual well-being of Christians caught in a broken and essentially nonexistent marriage justifies a divorce, with the right of one or both of the partners to remarry. Each parish priest is required to do all he can to help couples resolve their differences. If they cannot, and they obtain a civil divorce, they may apply for an ecclesiastical divorce in some jurisdictions of the Orthodox Church. In others, the judgment is left to the parish priest when and if a civilly divorced person seeks to remarry.

Those Orthodox jurisdictions which issue ecclesiastical divorces require a thorough evaluation of the situation, and the appearance of the civilly divorced couple before a local ecclesiastical court, where another investigation is made. Only after an ecclesiastical divorce is issued by the presiding bishop can they apply for an ecclesiastical license to remarry.

From GoArch.org

For Roman Catholics, Holy Matrimony is a binding, ostensibly an unbreakable, contract. The man and the woman marry each other with the "church" (bishop or priest) standing as a witness to it. Hence, no divorce under any conditions - no divorce but annulment of the marriage contract if some canonical defect in it may be found which renders it null and void (as if it never took place).

In Orthodoxy, Holy Matrimony is not a contract; it is the mysterious or mystical union of a man and woman - in imitation of Christ and the Church - in the presence of "the whole People of God" through her bishop or his presbyter. Divorce is likewise forbidden, but, as a concession to human weakness, it is allowed for adultery. Second and third marriages are permitted - not as a legal matter - out of mercy, a further concession to human weakness (e.g., after the death of a spouse). This Sacrament, as all Sacraments or Mysteries, is completed by the Eucharist, as St. Dionysius the Areopagite says.

http://www.orthodoxinfo.com/inquirers/orth_cath_diff.aspx

(Noting the assumptions on the Roman beleif may not be correct... )