A PICC (peripherally inserted central catheter) line is in the arm (or, in rare cases, in the leg) and a triple lumen catheter is a cental line placed in the chest. They are both types of central lines but the PICC line is (as its name suggests) inserted peripherally. PICC lines are placed more easily and it is often a bedside procedure and can be done by the IV nurse. Triple lumens are surgically placed in the chest (though I believe in the adult world or in ICU/code situations, they do sometimes place these at the bedside). In my experience, PICCs are used shorter-term (IV antibiotics, induction chemotherapy) whereas central lines are used longer-term (patients chronically dependent on TPN, long-term chemotherapy, stem cell transplant, etc).
Triple lumen just refers to the fact that there are three lumens to the line. Either a PICC or a CVL can be single, double, triple lumen. I think I've even seen a quadruple lumen CVL before.