Realm Exclusive Effect

People who live in a world much like ours where they are just average with nothing supernatural or extraordinary. While in another world, they have superpowers or certain items with powers, and when coming back to their world, their powers are usually inaccessible. The setting usually has two worlds that people can go from one to another, such as a portal, teleportation, a mystical artifact, or other means.

A staple trope of the Isekai genre.

Anime and Manga

 * Yumeria has a dreamworld called Moera where the character gains different outfits, powers, and weapons. The main character can also give the others in Moera a boost in power.
 * Averted in Fairy Tail where the characters are brought to Edolas and can't use magic unless they use certain equipment. This is solved when they swallow a crystal which allows them to use magic normally.
 * Yumeji, from Dream Eater Merry, has an ability called Lucid Gear that can only be used in a Daydream.
 * Played with in the manga Isekai Ojisan: when the titular character was dragged to a fantasy world, he didn't have any special powers there, but he was able to learn the local magic. Then he is returned to the modern world 17 years later, he still has the knowledge and can use magic.
 * El-Hazard: The Magnificent World, one of the earlier Isekai licensed for release in North America, has four people gain powers when they are transported from Earth to El-Hazard. (Which powers they get depends on which continuity they are in.) At the end, at least one of the people returns to Earth.
 * There's no evidence that the main characters of Magic Knight Rayearth get to keep their new-found abilities when they return to Earth.

Comic Books

 * The manfra, Dreamland, have people known as Traveler who gains access to the titular setting by facing their phobia and gaining a power related to it.
 * Amethyst, Princess of Gemworld in the original series featured Amy Winston, a normal teenage girl who travels to the magic-ruled Gemworld and transforms into Princess Amethyst. While on Earth, she's a normal girl without any powers, on Gemworld, she possesses the magical powers of the House of Amethyst.

Literature

 * In The Chronicles of Narnia, the Pevensies are just British kids living in the 1940s on Earth, but in Narnia, they're powerful kings and queens.
 * Also, to top it all off, their reputation in Narnia is similar to King Arthur's.
 * John Carter, in John Carter of Mars, gains superhuman strength and agility when he is teleported to Mars.

Video Games

 * Tokyo Xanadu has the Eclipse, which is an overlap of reality with the Spirit World where certain people can use armaments called Soul Devices that can be used against creatures called Greed.
 * Subverted in Persona 4 and 5 where the characters can summon their Personas while in the TV World and Metaverse, respectively. The characters within the setting believe that they can only summon them in the alternate dimensions. They can still summon them, but they would need to under heavy duress or the use of an evoker.
 * The Longest Journey has the two worlds of Stark and Arcadia that each have science and magic, respectively. A shifter can go between the two and have access to magic while in Arcadia. Stark favors science and technology compared to the use of magic in the Arcadia.
 * In Viewtiful Joe, the V-Watch cannot be used in the Real World and only in Movieland. To circumvent this limitation is through the use of being filmed by a V-Cam to transform with it.
 * The Mario Bros. in Mario & Luigi: Dream Team are as strong as they normally are in the rest of the Mario & Luigi series. But in the Dream World, Mario gains a mild boost to his stats and his regular attacks are turned into crowd-clearing AoE moves.
 * The Holy Instruments, from Dual Hearts, can only take form and be used by Rumble while in the Dream World.

Web Comics

 * In the Layers webtoon, certain teenagers can teleport to another world called Layer and have the powers such as telekinesis. Once someone becomes an adult, they lose the ability called Transfer that allows transportation to it.
 * Her Summon webtoon has a Summoner from another world summons Jin-Kyung from modern-day South Korea. While summoned, he gains magical powers through the use of objects brought with him. He uses these mundane items as a conduit for spells while the item gets used up as a battery would become dead and an insecticide gets emptied. When he is teleported back, he loses magic even when he tries a spell with an item that hasn't been used up.

Western Animation

 * Midnight Patrol: Adventures in the Dream Zone has the group and children and their dog are normal until they each have special powers while in the Dream Zone
 * Twelve Forever has the three protagonists who can teleport themselves to Endless Island where each has a unique power. Twelve get superhuman strength, Esther can create whips of light and transport made out the same material, and Todd is a shapeshifter.
 * Penn Zero: Part-Time Hero has the three protagonists take over for the heroes in the dimension that may be a hero with superpowers depending on who they overshadow.