Groot is dead. Baby Groot (now teenage Groot) is his child.
'Guardians' Director Drops a Groot Bomb He Thought Fans Knew, But They're Traumatized
Guardians of the Galaxy director James Gunn clarified this point during an exchange on Twitter. Gunn's responses suggest he thought it was always obvious and clear. The younger Groot in the sequel does not have the older Groot's memories and he has a different personality. Gunn also suggested that the older Groot's sacrifice in the first movie actually means something because he died.
Honestly, I hadn't put much thought into it before, but some folks are very unhappy about this. I'm going to have to run this one by my daughter to see what she thinks.