I think it's best when sequels reuse the same concepts and overall feeling while bringing in a new cast and setring, only merely leaving the door open for connections to be made. Vyk hit the nail on the head with Shining Force and it's kinda meta-cool how the connection between Shining Force I and II is made in a Game Gear game that very few people have ever played, making it a kind of lost secret, even among the fandom!

Metal Gear Solid 3 is a different example. Everyone knew it was Big Boss but the game very much held to the line that all you needed to know was that this is a different Snake in a different era.

A little bit borderline is Valkyria Chronicles II. It was the same country and era but while some of the characters from the first game made cameos, it was a different cast and a different war that stood on its own.