"Stretchable" or just elastic.

The most commonly known as "stretchy" abilities are these, an elastic character doesn't need to have everything here, but the main thing is that it can elongate its body great distances. A good representation for this category would be hard to point out, since often most elastic characters can morph and shapeshift their bodies as well as stretching. For example, even though Elastigirl from The Incredibles is usually seen using her stretching abilities, there's some scenes in the movie where she flattens herself on command, turns into a parachute and even morphs into a form of boat, feats that require some degree of shapeshifting to be possible. A better example would be Luffy from One Piece, who is basically only using his body's rubbery qualities in very unique situations for the first half of the manga, and then starts to combine them with the wacky shonen mechanics of his universe to go beyond that.
The way I approach this side is a character that has natural rubberiness to their body, but it's not necessarily made of rubber so electricity can still harm them, they also tend to naturally go back to their normal shape after any forced deformation like flattening or being shot by bullets. To me an elastic character can stretch their limbs using their own muscles to achieve it, they usually still have internal organs but they're just as immune to damage as any part of their body, if you cut them up they'd probably die like any normal person, unless you gave them regeneration abilities on top of elasticity.

"Malleable" or clay-like.

A malleable character usually focuses on the shapeshifting part of elastic powers, but can also stretch and deform, the main difference from just including any shapeshifting character is that their shapeshifting is often not perfect, so it's used more as a tool for combat or sneaking around since the transformations won't fool anyone in plain sight. This category has more examples since it's easier to give the elastic characters some degree of shapeshifting to be more versatile, but of course this isn't the only way this can be done. To name a few examples, first of all Plastic Man is usually known for his wacky shapeshifting powers but his transformations are often locked to his main outfit + body colors, which leads to the recognizability of the character, same applies to Jake the Dog from Adventure time. A more unique case would be Inque from Batman Beyond, a shapeshifting villain inspired by Clay-face from the original Batman comics, except she doesn't shapeshifts into perfect replicas of other things, but is actually locked to a pitch black + blue color palette that takes advantage of the gothic art style of the show to blend in with the shadows, while still using her body's natural liquid malleability for combat.
The way I approach this side is a little different from most media examples, I like calling it clay-like because they have similar attributes to clay, basically you can do anything with their body that you could with a lump of clay, deform, stretch, grow new limbs, cut them up and rearrange their body parts, it doesn't matter to them as long as they have their mind intact, admittely this sounds a bit overpowered, but in contrast to elasticity these characters have to keep concentration and learn to manually go back ot their natural shape, as well as being prone to the typical weaknesses of clay like baking in the sun or water making them too malleable to hold together, this is just my interpretation though, so make sure to experiment with different ways of making unique malleable characters.