Is a "2 GHz Intel Core Duo" really the same as a "2 GHz Intel Core ***2*** Duo"
Yes, the Core 2 Duo and Core Duo are different and the Core 2 Duo came later so your iMac should support any software that requires at least a Core Duo.

You can tell because the Early 2006 MacBook Pro used the Core Duo while every MacBook Pro after that until 2010 used a Core 2 Duo. This isn't definitive in proving that the Core 2 came after the Core, but Apple's not going to continually downgrade the processor in its top-of-the-line laptop year after year, plus the "2" usually denotes a successor anyway.