Prenuptial agreements occur prior to two persons getting married and can address property and support issues prior to their wedding.
A marriage contract occurs once two parties are already married. This can occur at any point during the marriage. If you were unable to compete a prenuptial agreement before getting married, you can still proceed with a marriage contract.
A cohabitation agreement is ideal for couples intending on moving in together but do not have any plans for marriage. Typically, these agreements are considered marriage contracts in the event that the parties marry at a later date.