First of all I would be careful using the abbreviation CCU as it generally stands for cardiac care unit and not critical care unit as I think you intend it to be.
During my education We had some lessons about the different levels of care. From what I remember is that terms like high dependency units, medium care, step-down units, special care units are all kind of the same thing.
HDU's and all others are generally considered areas where patients are being nursed and monitored that have a real possibility of single organ failure or are in single organ failure that requires supportive measures (either farmacologic or mechanical). The only thing that isn't regularly done in these units is mechanical ventilation via endotracheal tubes. This latter is reserved for the intensive care units. As a result in these units there is a nurse : patient ratio that is higher than the general wards and lower than ICU.
Intensive care units can take in the same patients as the HDU when for example there is no HDU available in the hospital or because there is no room for such patients in the HDU. On top of that ICU generally takes care of patients that have a real possibility of multiple organ failure or are in multiple organ failure that requires supportive measures. They also take care of mechanical ventilation via endotracheal tubes. These units know the highest nurse : patient ratios.
Now this above classification is all nice and well but in the practical terms it depends a lot on how the hospital decides to organize things.
In my hospital for example we have several HDU's we have a cardiosurgical medium care, neurosurgical medium care and thoracovascular surgical medium care, a CCU (in my hospital they are classified as a medium care), and a chest pain unit (CPU) that is attached to the ER. But there is no general medium care so some specialties only have a choice between general ward and ICU for their patients.
And even in between the different medium care units there is a difference in their scope of practice. And some patients that require medium care are nursed in the general wards (e.g. non invasive ventilation is either done in the pneumo ward or in the ICU). E.g. the neurosurgical medium care will use IV antihypertensives to titrate blood pressure but won't use any vasopressors or inotropes. In the cardiac oriented medium care units vasopressors and inotropes are used in moderate amounts.
I also know of hospitals where CCU is an equivalent to an ICU where they'll take in any unstable cardiac patient no matter what their pathology. They'll have vented patients with IABP's, LVAD's etc. I can't imagine us arriving in our CCU with these kinds of patients ^^.
At the same time there is also a big difference between acuity in ICU's depending on the hospital. Bigger hospitals generally have more facilities available and will see more acutely sick patients that require HDU or ICU care. We see this a lot when we are called to transport an ICU patient from a smaller ICU in another hospital to our ICU in the university hospital. Often times we are collecting their sickest patient and that patient is in our terms only moderately ill when compared to the really ill patients we have back at our ICU.
Depending on the country you are in there are generally classification systems for the hospital in general and the ICU's in specific.