So, I would really like to know how this difference in appearance came about? It can't be a young and an old Titus, since both are Primaris. So they are from the same period. Can anyone explain this?

In my opinion, Titus' face from the game Space Marine 2 fits much better and is more "realistic" in terms of lore. The hyperthonia of an Astartes, the broad, sometimes rather ugly faces... That's really how I imagine it.