One of the main differences between Guardians of the Galaxy and Guardians of the Galaxy: Volume 2 is the way the character Groot is portrayed. In the original film, Groot was the team's enforcer; a massive living tree who was practically unbeatable in a fight, but who still had a childlike sense of wonder and a heart of gold. After his sacrificial destruction at the end of that film, he came back to life as a baby, and he's still a baby in Guardians 2. But is Baby Groot the same Groot?
The new film never explicitly reveals whether or not Baby Groot is the same Groot, but there's really no reason to believe he isn't. It's established early on in Groot's first appearance in Guardians of the Galaxy that he has regenerative powers, when Rocket says something about his arms growing back after having them hacked off by Gamora. And of course, they are later seen fully restored. So going by the logic that Groot is essentially indestructible, it seems evident that if he is blown to bits — like he was in the first film — then a piece of him would have the potential to regenerate into his full body, and that's exactly what fans can see happening in Guardians 2.
There is also precedent for this in the comics. Since making his modern debut in 2006, Groot has died no fewer than three times while sacrificing himself for the good of the team, with his most recent demise occurring during 2015's "Secret Wars" event. Each time, Groot has been able to fully regenerate to his complete former self from a twig, and every time it's been implied that it is the same ol' Groot once he's recovered.
The Baby Groot of Guardians 2 does act a bit different, though, and that's because of his age. While he is still the same Groot, he's basically a toddler, and therefore has to relearn how to be Groot again. He's the same guy, but he's essentially reliving his life. I assume he probably retains his old memories — he's not weirded out by Rocket Raccoon or anything — but he needs to develop his motor skills, life skills, etc. just like a child would.
Baby Groot may seem like a completely new character in Guardians of the Galaxy 2, but rest assured, he's the same Groot you fell in love with from the first Guardians.