iMessages are Apple's own Messaging service.
The iMessages leave your iPhone (or iPad or Touch or the Messages Beta on a Mac) and go to Server and from there to your Contact.
SMS goes to your Carrier, through their server and to the Contacts Carrier and then to the contact.
MultiMedia texting tends to include pics or files where as SMS does not. (however this does vary carrier to carrier)
iMessages can also do Group "Chats" and can send pics or some files.
iMessages can be set up to "Send" from an Apple ID or from the iPhone Number (See Settings > Messages > Received At > Caller ID)
Whether your contact shows the Name in their Address Book or the ID or number you sent from will depend on what is on their Card for you. If "your" card shows only the iPhone Number and you are sending for the Apple ID they will see the Apple ID and not your Name as they are not associated in the Contact List/Address Book.
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Lion 10.7.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
"Limit the Logs to the Bits above Binary Images." No, Seriously