'Wedding' means the actual ceremony while 'marriage' is the general relationship. 'Marriage' (or 'married') depicts the relationship status of a person.
Wedding refers to a ceremony that binds two people in the bond of marriage for a lifetime. Therefore, the correct way to say it would be “you are invited to my wedding” and not, “you are invited to my marriage. ” 'Marriage' is an institution which starts after the 'wedding' (the ceremony).
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