I’ve heard that a separation agreement is separate to all the other agreements. Is this true?

A separation agreement can be a separate contract, or the court can adopt the agreement as its own order as part of the divorce or separation judgment/decree. When this happens, the agreement is said to be "merged" into the judgment/decree.

If it stands alone and is essentially only referred to in the judgment/decree, it is said to be "incorporated" or "incorporated by reference" into the judgment/decree.