The difference is that the CMM is a way to communicate capabilities, and ISO is a way to communicate the process. They are not necessarily incompatible.

The Capability Maturity Model is a very specific way of classifying an organization's software development methods. In a certain way, it tells how the quality of its softwaredesigns is likely to be repeated.

ISO-9000 procedures describe a (possibly) definite development process but gives no indication of the likely quality of the designs or whether multiple software efforts are likely to produce software of similar quality.