Sure. As mentioned, I think, gezhe refers to Chabad chassidim who are part of a family chain (geza) of chassidim going way back. Usually used in comparison with terms of ffb, bt, yichus.
All Chabad children go to the same schools, seminaries, yeshivos etc, and can go on shlichus, depending on how badly they want to go, without distinction. The only time it really comes up is with shidduchim, and that is fair.
There is an advantage to families being compatible, if I would’ve married into a gezhe family, I wouldn’t feel my parents are on equal footing with my supposed in laws and that can get awkward.
My parents are amazing incredible people who turned their whole lives around to because frum and that is their advantage because they passed over to me the conviction that yiddishkeit is the best thing out there and the goyishe world is so empty, it has nothing substantial to offer me.
Otoh, I can’t compare their aidelkeit to the aidelkeit of a gezhe family…
There is also a difference in upbringing: gezhe people mainly raise their kids to toe the line of their ancestors, whereas BTs focus on rebelling against or revolutionizing the secular world…
But many gezhe people are open to their kids dating bts kids, just the bt background is understandably not seen as a plus in family compatibility.
As far as other differences, no unique minhagim other than family minhagim like what they can eat on pesach.
Hope this clarifies