How does a contract differ from a service invoice?

A contract is simply an enforceable agreement, thus an invoice or work order to which all parties have agreed is a contract (although it should be clear that it is a binding agreement; if it says something like "this is an estimate only", there could be problems).  The same defenses applicable to any contract are applicable to it, e.g. it was signed under duress, it was procured through fraud, one of the parties lacked capacity, the terms were not sufficiently clear and definite, etc. etc. Most contracts do not have to be in writing to be enforceable, although it is obviously much easier to prove the existence and terms of a contract if it is in writing.  Even where a contract needs to be in writing, however, it is generally sufficient that the writing be signed by the party to be charged.  In other words, if you are suing the customer for breach of contract, it would probably be sufficient that he/she/it had signed; your signature would not be required, but would be required if the customer were suing you (although your letterhead on the top of the invoice would likely be sufficient). In some cases, a statute requires that a particular class of contract must be in writing signed by both parties, e.g. a prenuptial agreement.  The agreements you're talking about don't appear to fit in this category, but I am not a North Carolina attorney and so can't be sure.  More often, the parties themselves do not agree to be bound unless both parties sign, and this is usually reflected in the writing itself.  Thus the document itself will state that there is no contract until and unless both parties sign.  In such a case, both parties would need to sign before a contract is enforceable.