Yes I think they are 2 different families, but the most certain way to follow your line ancestors is ofcourse to go back in time from father to son.
But I'm quite certain it's about two different families,
f.e. my ancestor familiy name is Nuijs, there is also a familiy line 'van Nuijs'' but they are two very different families.
It's not unusual that with or without ''van'' are different families.
You know were your Guurtje van Ingen ''mother'' came from?