As far as the franchise's narrative and continuity are concerned, yes, it's unequivocally a different Link, 100 years after who we presume was his ancestor - the Hero of Winds, the WW/PH Link - helped discover the new land and rechristen it Hyrule.
As far as the physical, technical, character and mechanical aspects - the things that really matter to a video game - are concerned, it might as well be the same Link for all the difference. He's young, short, wide-eyed, plucky and just raring to get out there, brandish a sword, rescue a princess and save Hyrule. So while it's technically a different Link, it's a different Link who looks, acts, plays and controls identically to his ancestor.