By using either 時{とき} or 頃{ころ} you are describing a time relation between (at least) two events, states, or actions (let's say A and B).
With 時 the relation between A and B is closer like English "when", "while", "at the time". With 頃 the relation is more vague like English "around the time", "around".
Just like in English you can also use 頃 to express not only the sheer relation, but also your attitude (you don't remember exact order of actions or their relation, our you don't want to provide such information, so you say "around the time").
With naturally vague expressions ("in youth") 若い頃 or 若い時 it's just a difference in style.
It does not matter if either A or B is a point in time or a period of time. However 頃's vagueness creates a span of time in which the relation between A and B occurs.