Type 2 usually wear their beta cells out unlike type 1 which is caused by an autioimmune reaction. That is why there is a separate distinction between the dieases.
http://en.wikipedia.org/wiki/Diabetes_mellitus_type_1
So, no, I don't believe Type IIs simply wear out their beta cells. There's something else at work ~ with a genetic link ~ that slows beta cell insulin production.