Except it's not, it's a call to end segregation and create one free, secular and democratic nation across the entirety of the original territory of Mandatory Palestine. Apartheid South Africa also segregated native peoples into tiny enclaves as a form of democratic suppression, and that was resolved by creating one free and democratic nation:

That's part of why South Africa was the nation that brought charges of genocide against the Palestinians to the ICC. It's also why outspoken zionists like Elon Musk have recently tried to condemn "racism against white people" in South Africa.

Edit: I will say, you are correct that both sides use it, though Palestinians (and their allies) will always include "Palestine will be free" at the end, and that supports my above statement. However, when the Israeli side uses it, they make clear that the one nation would be Israel, which is specifically a Jewish state to the exclusion of other religions.