People become "engaged [to be married]" before they actually get married. The engagement period can last from a few months to several years. When a couple decide that they want to marry, they get engaged first (he woman usually receives an engagement ring to wear on her ring finger). They might have an engagement party and receive cards and presents to congratulate them. Then, an unspecified amount of time later, they get married. This time they get a ring each to wear on their ring finger, and they have the wedding ceremony, a party (called a wedding reception), more cards and presents and then go on honeymoon.
That's the traditional way at least.
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