Though they can behave casually and calmly towards each other, Sanji very frequently gets into physical and verbal fights with Zoro (who he refers to as “marimo” or “mosshead” because of his green hair); in turn, he is nicknamed “shitty cook”, “ero-cook” and “Prince of Dumbass Kingdom” (among other things) by Zoro.
Although he spends a lot of time arguing or competing with Zoro, Sanji is not beneath siding with Zoro on those rare occasions where Zoro has seen the bigger picture more than everyone else (e.g. on their preference for death rather than dishonor during the Davy Back Fight, and on Usopp rejoining the crew). He also tried to stop Zoro from sacrificing himself to Kuma to save everyone else by offering his life instead, although the swordsman knocked him out first before he could do so.
After waking up to find Zoro missing, he showed great concern at what may have happened to him, and was the first to find Zoro in the aftermath of Kuma’s attack.
Furthermore, although their rivalry sometimes impedes their effectiveness during battle, once the two agree to work together against a common foe, they are nearly an unstoppable team.
Despite their comical fights and rivalry, they have a brotherly trust and care between them they would never admit to, in fact the two warriors understand each other better than other crewmates.
After Wanda accidentally implied that the minks had killed the Curly Hat Pirates, it is Zoro who calms the others down by reminding them that Sanji was with them, and that he would not have let his half of the crew get killed.
Because of their mutual respect for, and dependence upon, each other’s strength, Zoro initially refused to forgive Sanji for leaving the crew on Zou and allowing himself to get dragged into the affairs of one of the Yonko. He also acted like he didn’t care what happened to Sanji, but Luffy caught him listening to Pekoms as the mink explained Sanji’s predicament with Big Mom and his family; this caused Luffy to assume (correctly) that the swordsman was in fact worried about Sanji.