In Yevamos 33b, the gemarra is trying to figure out what part of the Temple service would constitute a Shabbos violation if a non-Kohen were to do it. The gemarra suggests throwing the animal limbs on the altar (הקטרה), but rejects that because the gemarra is discussing Rabbi Yossi, who holds that burning a fire on Shabbos (הבערה) isn't a bona fide Shabbos violation that results in kares/an obligation for an offering. Rather, it's simply a prohibition worthy of lashes. The gemarra therefore suggests something else.
I was very bothered that why isn't הקטרה considered the Shabbos prohibition of cooking? The meat gets cooked in the altar fire. I then noticed that Rabbi Akiva Eiger there says Yerushalmi Shabbos 2:5 teaches a dispute in this. Rabbi Yehudah says that הקטרה is the prohibition of burning a fire on Shabbos, and Rabbi Yossi holds הקטרה is the prohibition of cooking. They seem to be arguing if something I want to get cooked but not eat is the violation of cooking on Shabbos, but I could be misunderstanding.
Why didn't the Bavli gemarra say this as well? Subsequently I found that the Nishmas Adam 20:2 says that in a dispute Rabbi Yehudah and Rabbi Yossi, we go with Rabbi Yossi. The conclusion of the Yerushalmi would then be that הקטרה is cooking. However, he infers from the gemarra in Yevamos that we started with that the Bavli disagrees, even according to Rabbi Yehudah (?).
What's the dispute between the Bavli and the Yerushalmi?
