One of the most unusual things regarding the Lufia series is the fact that Lufia 1 and Lufia 2 do not share a world map. The two games take place only one hundred years apart in the exact same world, but other than Doom Island itself the two games don't share any of the same locations at all. I can understand why the game designers might have wanted to do this, since using the exact same world map in multiple games can be overly restricting, but it is somewhat jarring without good explanation. Lufia 2 hand-waves the change off by saying that the two games take place in two different regions of the same world, but this is somewhat of an odd way of doing it when both games give you an airship that lets you travel freely and circumnavigate the entire map. Having the ability to freely fly around the entire known globe and loop the edges gives the impression that the area displayed on the world map really is the entire world, which makes it seem like the game is contradicting itself when an NPC says that such a world map is only a single region.
A similar odd situation is seen in Chrono trigger's sequel, Chrono Cross. Presumably, you have explored the entire world already in Chrono Trigger (in many different time eras, no less), but Chrono Cross exists in a place that is somehow outside of Chrono Trigger's world map. The game takes a few measures that makes it a bit less jarring than it was in Lufia (no airship travel in the sequel and a few nods to powerful factions trying to prevent that region from interfering with the events of Chrono Trigger), but it still feels forced.
That said, the "different region" explanation itself can work very well if used correctly. For example, each game in the Suikoden series uses a completely different set of locations for each of the games, even though all but one of the entries in the series are separated by a few decades at most, and many characters appear in multiple games. However, unlike in the Lufia games, the different regions are really treated like smaller pieces of a much larger world. Most games only take place in a single country, the regions are given limited boundaries, and the player is almost never allowed to travel beyond the edge of the main region in any way. In addition, the games contain many references to distant lands that the player can't ever visit within the scope of a particular game. For example, the Queendom of Falena was referenced in Suikoden 2 in a few minor places, but it took until Suikoden 5 for one of the games to actually take place in that country. Another place mentioned several times since Suikoden 2, Kanakan, has yet to actually appear in a game. Because these places have been partially described in several places and have a lot of relevance to many characters' stories, they can be very interesting even when they are not seen. More than once I have found myself looking forward to the day a Suikoden game would take place in a particular region.
One alternative to the "different region" idea that accomplishes a similar effect is seen in the transition between Breath of Fire 1 and Breath of Fire 2. The two games share a few locations and the general shape of the BoF2 world maps is similar to the original game's map, but they also have a large number of differences. In fact, BoF2's map looks a lot like a version of the BoF1 map with higher ocean levels. They are the same world, but because the designers didn't specify how much time took pace between the two games it is possible to simply assume a long time has passed and the world has changed somewhat. The rest of the Breath of Fire games use different variations of this. The games share some locations, but the connections between the games is left vague, and in the case of BoF3 the map is far from complete, so vast changes to the landscape can very easily be hand-waved away as being the result of events that take place between the different games (if you can even prove that the games are connected at all). The jarring effect of the changes between Lufia 1 and 2 is not seen here, because the world itself is not as clearly defined as it is in the Lufia games.