No, it's not about "Gazan vs Palestinian". It's that Arabs sometimes refer to someone using his city. For example, if someone is from the city of Khalil (Jericho), he might be called as "khalili", people from Nablus as nabulsi. This is a trend in most Arab countries, in Jordan, people from city of Maan refer themselves as Maanis, from Irbid as irbidawi, etc...