A dissolution of marriage is Connecticut’s legal term for a divorce. It happens when two people have been legally married, and one or both of them goes through the court process to have the marriage ended. Orders about alimony, division of property, name changes, child custody, visitation, and support can all be made in a divorce.
A legal separation is a court order between married people. It is similar to a divorce in that the court can make orders about money and children. But after the court orders are put in place, the people remain married. This is usually done for religious reasons, when people cannot stay together but do not feel right about divorcing.
Sometimes when people say they want a legal separation, they really mean they want to get court orders and start living separately, and decide at a later date if they want to file for a divorce. Some people may file a case that asks for both a divorce and a legal separation, and decide later which will be the final order. If one person wants a legal separation and the other person asks the court for a divorce, the court will order a divorce.
An annulment is a court order that says that a marriage never existed in the first place. Many people think they can ask for an annulment because they have been married for a very short time. An annulment is usually only possible when the marriage was not legal in the first place (for example, if one of the people was underage or already married).
Some churches have a separate "annulment" process, which is the name they give for granting religious permission to end a marriage. That is not connected in any way to the state laws or processes about marriage.