In most cases, when a game receives a sequel, the sequel exists within the same genre as the previous entry or entries. However, this is not always the case. Sometimes, though the game may be a sequel in terms of plotting or by name, the actual game itself may exist in a genre different from those that came before.
Although technically, most of these games don't actually apply to that idea, as they are spin-offs, not real sequels, it's still a fun concept, so some examples are listed below.
Even though World of Warcraft is not a direct sequel to Warcraft III: Reign of Chaos, it is in fact a continuation of the storyline and takes place in the same universe. Instead of ordering heroes and units around on a battlefield, players are now able to create their own hero and take on quests to create order in the world of Azeroth. Over the years, several of the game's antagonists have fallen, and with the 2008 expansion pack World of Warcraft: Wrath of the Lich King, the main plot-line of Warcraft III: Reign of Chaos came to an end when players assaulted Northrend in the pursuit of Arthas.
Like its predecessors, Shin Megami Tensei: Persona 4 is a party-based RPG with turn-basd combat. However, the direct sequel to the game, Persona 4 Arena, is a one-on-one fighting game. Though the change in genre is drastic, Arena maintains close ties Persona 4, as well as Persona 3, with an intricate storyline that follows the events of both games and leaves plot hooks in place for Persona 5. Arena also contains numerous stylistic and aesthetic references to the RPGs, with elements such as the characters' Personae, status effects, All-Out Attacks, and so on having been incorporated into the fighting system.
After nearly two decades since the release of Kid Icarus: Of Myths and Monsters, a side and vertical-scrolling platformer, Nintendo released Kid Icarus: Uprising. Unlike its predecessors, Uprising does away almost entirely with platforming. The player character Pit cannot jump, save for the use of special floor pads. The game also features on-rails flight sequences in most stages that are reminiscent of such games as Space Harrier or Rez.