I may need to put this in another topic, but I'm not clear on what a "signed message" is.
My understanding is that a message can be included in a transaction, which goes into the block chain. Is this what you are referring to as a "signed message"?
No that is a transaction and you can't (without some really bad hacks) include a message in a transaction at least not in any standardized easy to decode method.
Transactions are not messages. Messages are not transactions.
Is there such a thing as a signed message that is not part of a transaction in the block chain?
Signed messages are never part of a transaction and never added to the blockchain.The client has the ability to sign any arbitrary text. Once again this has absolutely nothing to do with transactions.