Here is my attempt at explaining it.
You can get a CPL/IR, by studying for the CPL ground exams, studying for the IR ground exams (I think), and doing the CPL and IR flight training (obviously you will meet the requirments to do the CPL and IR in terms of flight hours etc). Thats it. You can't get a job in the airlines, well, at least not in JAR land.
If you sit the ATPL exams, and do the CPL and IR flight training(again, obviously you will meet the requirments to do the CPL and IR in terms of flight hours etc), then you have a frozen ATPL (informally abbreviated to fATPL), which still is a CPL/IR. When you reach the requirements for an ATPL, your fATPL will be unfrozen. You can get an airline job with an fATPL, and usually airlines like you to have an MCC, although I have heard a few stories of airlines not requiring an MCC since they give you the MCC training.
You can get paid jobs with just a CPL, such as flight instructing, but you must additionally obtain a Flight Instructor's rating.
Hope this helps.