DRGs are a system to classify hospital cases into a diagnostic group for Medicare as part of the payment system. DRGs are used to determine how much Medicare pays the hospital, since patients within each category are similar clinically and are expected to use the same level of hospital resources. DRGs are also used to collect data on the number of patients with certain diagnoses and can be used to allocate resources (ie, if a hospital notices that they have many more patients readmitted with COPD, they may start to think about allocating more resources to outpatient Pulm clinics).
CPT are codes for procedures or operations done on patients. All patients will have a DRG, not all will have CPT codes.
As a surgeon, when I operate on someone I document the CPT code and that's how I get paid; the hospital documents their DRG and that's how they get paid. Of course, if I don't actually operate on someone (ie, admit for a post-op complication or other non-surgical reason), I don't submit a CPT code (but I still get paid for my services).
Hope that helps.