What happens when age of majority is >18? (legal)

Duckster’s post in another thread alerted me to the fact that the age of majority is not consistent throughout the US. Specifically, it’s 19 in Alabama, Nebraska, and Wyoming, and 21 in DC and Mississippi, according to this page. But what does that actually mean? Everyone can vote at 18, thanks to the 26th amendment. None of the states allow drinking before 21. According to the same page I cited, some of the states with higher ages of majority allow marriage without parental permission at 18. None of the state ages of consent are above 18.

So what do the higher age of majority laws actually affect? As a 20-year-old, how would things be different for me if I moved to, say, Mississippi after already being considered an adult for a couple years in most of the rest of the country? Would I be able to sign a lease? Open a bank/credit card account? Give consent for medical procedures? Sue somebody? Would my parents suddenly be legally responsible for me again? If there was someone paying child support for me who stopped when I turned 18, would s/he have to start paying again? Would contracts I’d signed in another state as an adult be unenforceable in Mississippi? Would any of these things be different if I’d always lived in Mississippi? If those things aren’t different, what’s the point of an age of majority above 18 anyway?

As I highly doubt I’ll be even visiting those states anytime in the next six months, I’m not looking for serious legal advice. I’m just curious.