welcome to the wonderful world of New Netherland "surnames", where the possibilities are endless. I've been working with Welsh names most recently, so I'm a little rusty on Dutch patronymics, but yup - sen, son, and even just "s" turns Dad's given name into an identifying name for his children. So, for instance, Jan Joosten (John, son of Justus), might have a son named Joost Jansen (Justus, son of John). Or the son might just be shown as Joost Jans in records. New Netherland names have the added fun of being recorded by the English after 1674.
When I first started working on New Netherland profiles, my mentor offered the following explanation, which you might find of interest:
This is my current understanding. Replace [Jan] with any father's name. The meaning of the patronymic is [Jan]'s son or [Jan]'s daughter. In formal Dutch this is [Jan]szoon or [Jan]sdochter, where zoon = son and dochter = daughter. Note that the 's' following the name is a possessive 's'. These are sometimes abbreviated [Jan]sz(n) or [Jan]sd(r), where the (n) and (r) are optional). You see this form in the very earliest New Netherland records, but about the time of the New Netherland settlement the Dutch started spelling 'zoon' as 'sen', and at the same time using it for both males and females. Note that in Dutch 'oo' is pronounced like the 'o' in go, not the 'oo' in zoom, so 'zoon' and 'sen' are not pronounced very differently. With the new spelling, [Jan]'s son would be formally spelled Janssen, a form you often see. But often the double 's' is contracted to a single 's', and 'sen' is contracted to 'se' or 's'. All of these forms are found in the records for Joost Janssen. Given all of that, all the following patronymics are correct for Janssen: Janszoon, Janszn, Jansz, Janssen, Jansse, Janss, Jansen, Janse and Jans.
Hope that helps!