Facebook blocking?

Okay so this probably a stupid question, but I was wondering if someone blocked you on Facebook messenger but not on Facebook itself, and you go and block the person who blocked you first completely off the app. Can the person who blocked you on messenger go back and block you on Facebook as well even when they are blocked ? 

I’m just asking this because I was blocked by a former friend of mine just on messenger and I ended up just blocking him completely off the app, but on messenger his name doesn’t show as blocked even though other accounts do and when I go onto Facebook it shows he’s blocked so I’m just confused.