I think
@Charlotte Horchata knows the difference from talking with them. The idea is that while Zoro is certainly, 100% portrayed as Luffy's right hand man:
- Urouge's definition on Zoro was "2nd Hand", not First Mate. It was translated as first mate by VIZ, but Urouge doesn't actually call him "Fukusenchoo", he calls him "Niban Te", literally "2nd Hand"
- Bartolomeo 100% calls Zoro "Fukusenchoo", but he explicitly says "My voice/words/belief/opinion/etc" (he says "Ore no koe") in the midst of claiming this.
I get where they are coming from, but this point, its really just discussing silly semantics about these characters though. The Strawhats are all friends at heart and there is zero command hierarchy in the end because Luffy listens to the demands of his crew and follows through (Law was entirely confused by this at PH lol). Clearly Zoro is Luffy's right hand man, pretty much functioning as the "Vice Captain". Luffy himself is a pretty shitty Captain too, and none of his crewmates even treat him as such lol.