Adding to Marsha's hypothesis: all of the records for Gittel Kurz's children in the screenshot appear to specifically note that she was born in Jezierizany. That may be another data point in favor of the guess that there were two Alter Kerns in Czortkow: one married to Gittel Kurz from Jezierziany, and one married to Chaya Rost (presumably born in Czortkow itself, since there is no notation specifying a different town of birth).
There are at least a couple of complications here:
-one is that the original page from AGAD, the Polish State Archives, is badly torn on the page recording the death of Sosie Kern, daughter of "Chaya Rost". (Click "view image" to bring up that page.)
-another is that there are actually most likely earlier records than this for the children of Gittel Kurz of Jezierzany. If you search for just the surname Kurz and the town of Jezierzany you'll bring up birth records for Chajem Ellie and Chaje "Kurz", twins born in 1877 in Czortkow with no father's name indexed. That to me looks like another point in favor of there being two different Alters - assuming Chaya Rost's name has been correctly recorded, it strikes me as relatively unlikely that Chaya Rost would have had a daughter with the same name (Chaya).
-One big question is how to reconcile the guess that the two Alters were first cousins with the death record showing the Josef Isaac/Alter who died in 1887, age 40. The reason is that that Alter is clearly the son of a Chaim Elia. The straightforward guess would be that this is your gg-grandfather and that your great-grandfather Hyman was himself named for his father's father (who had the same name). Except...assuming "your" Hyman/Chaim Elia was definitely born around 1872, then how do we explain the Chaim Elia, likely the son of an Alter Kern, who was born to Gittel Kurz of Jezierzany in Czortkow in 1877? If there were two different Alters and they were first cousins to one another, the Chaim Elia born in 1877 would almost certainly not be named for his own grandfather: that would imply that there were two brothers who both had the same name (Chaim Elia).
Maybe looking at more of the original pages, as well as those for other Kerns from Czortkow, will help clarify whether there were indeed two Alters and whether they had some more complicated relationship than first cousins (i.e., second cousins, uncle and nephew, etc.)?
Adam Turner