Pathological or compulsive hoarding is a specific type of behavior characterized by:
acquiring and failing to throw out a large number of items that would appear to have little or no value to others (e.g., papers, notes, flyers, newspapers, clothes)
severe cluttering of the person's home so that it is no longer able to function as a viable living space
significant distress or impairment of work or social life
I'd say collecting if we are going by the definition.