What is the difference between hemodialysis & peritoneal dialysis?

"Hemo" means blood. Hemodialysis is when the patient's blood passes through a dialyzer (where the wastes and extra fluid are removed from the blood). This dialyzer is attached to a dialysis machine. A hemodialysis treatment usually takes around 4 hours and occurs 3 days/week. It is the most common type of dialysis.
With "peritoneal dialysis", a dialysis solution is placed in the peritoneal cavity (via a catheter). The person's wastes and extra fluid then pass from the patient's blood directly into the peritoneal cavity and then later removed via the catheter. Peritoneal dialysis is usually done at home.
The term "acute dialysis" usually refers to dialysis that occurs when a patient is in the hospital (when "acutely" ill).

"Hemodialysis
Main article: hemodialysis
In hemodialysis, the patient's blood is passed through a system of tubing (a dialysis circuit) via a machine to a semipermeable membrane (dialyser) which has dialysis fluid running on the other side. The cleansed blood is then returned via the circuit back to the body. Ultrafiltration occurs by increasing the hydrostatic pressure of the blood in the dialysis circuit to cause water to cross the membrane down a pressure gradient. The dialysis process is very efficient, allowing the treatment to be undertaken intermittently, usually three times a week, but often fairly large volumes of fluid must be removed in a session which can sometimes be demanding on the patient.

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Peritoneal dialysis
Main article: peritoneal dialysis
In peritoneal dialysis, a special solution is run through a tube into the peritoneal cavity, the abdominal body cavity around the intestine, where the peritoneal membrane acts as a semipermeable membrane. The fluid is left there for a period of time to absorb waste products, and then is removed through the tube. This is usually repeated a number of times during the day. Ultrafiltration occurs via osmosis in this case, as the dialysis solution is supplied in varying osmotic strengths to allow for some control over the amount of fluid to be removed. The dialysis process in this case is less efficient than hemodialysis and is carried out daily, but the ultrafiltration process is slower and gentler."