For Catholics, if the marriage didn’t take place in a Catholic church, it’s not a valid marriage. If a marraige ceremony does take place in a Catholic church, it is a valid marriage.
California can label their partnerships anyway they want, but a Catholic marriage will always be a sacrament that will always be labelled a Catholic marriage.
The Catholic Church recognizes the marriages of non-Catholics as valid; and the marriages of baptized non-Catholics as valid and sacramental.
Otherwise, you could have Catholics running around getting married to other people's spouses, and then saying, "But it's OK, because they weren't really married." This is false.
Marriage was instituted before Catholicism, before Judaism even, at the dawn of the human race. What it requires is a man, a woman, the sincere consent to marry, and natural intercourse, the act which consummates marriage.
However, if either partner is a Catholic, the Catholic is bound by the requirement that Catholics be married in the Catholic Church. Otherwise the Catholic Church will not recognize the validity of the marriage.
In other words, the Catholic Church is saying, "We recognize that all kinds of people --- not just Catholics --- get married. We respect that. But if you ARE a Catholic --- then hey, buddy, your are obliged to be married in the Catholic Church."
Catholics who are married outside the Church--- possibly because of ignorance of the requirement --- and then want to make things right, usually do not have any difficulty in getting the marriage covalidated (blessed.)
You're right in saying the State has no essential role in this.
You'd also be right in saying that under no circumstances could two men or two women do this (marry), because same-sex people cannot do the marriage-defining act: have natural intercourse with each other.