[BOTW] Is BOTW link different from age of calamity link?

Now I know they are the same link, who go against the same guy... "kinda" but link doesn't really interact with the wild in age of calamity, and isn't placed 100 years in the future, like this one is way different then what BOTW link went through, but he's still the same guy right? Is he labeled as a different "Hero of ___ " or is it the same? Because they seem awfully distinct, but are the same person.