I think the best way to describe the difference between these two methods is by discussing the two completely different approaches. One significant difference is that CCPM takes into account both task and resource dependencies. CPM, on the other hand, does recognize task dependencies, but does not consider resource dependencies and this is a very significant difference. As a result, CPM's Critical Path looks much different than CCPM's Critical Chain. Although this may seem like a small difference, in reality it is a major difference.
CCPM eliminates bad multitasking by scheduling resources based upon project requirements. That is, CCPM will actually delay the start of a new project to accommodate conflicting resource requirements. To this point, CPM users believe that to complete projects sooner, they must be started sooner, but this is not a valid assumption. CCPM users believe that in order to complete projects sooner, they must be synchronized which means that sometimes project starts are delayed.