Figured I would start a new topic rather than continuing this on the release thread to get more exposure. Issue is on original Droid 1.
The following seems to occur no matter the messaging app, such as the built in text message app or facebook messenger. Haven't been able to test with Google Voice, but in the past it was giving me the wrong ringtone as well (it is usually left closed).
When I leave the app open I get the correct notification ringtone.
When I close the app (by pressing the home button) I get a ringtone that sounds like a digital phone ringing.
Seems to not matter whether the phone is locked or active. Appears to be related to the messaging app being open or closed.