I've watched "Avengers: Age of Ultron" many times, and I've watched the X-Men movies even more. Besides that, I've been reading the Marvel comics, watching the cartoons, playing the video games, and nerding out to the movies since I was seven years old. In terms of the mutants of the X-Men series, I have researched and researched, and researched some more. As a result, I have a, um, studied knowledge base regarding their powers.
Quicksilver and the Scarlet Witch, both of whom were featured characters in "Age of Ultron," are mutants originally. However, in the movie, they are the result of science experiments, not unlike Captain America. Scarlet Witch's (S.W.) mutant ability is the ability to manipulate probability and cause unlikely and unnatural things to happen, as if by magic, just like a witch. Her power eventually develops to reality manipulation, where she can reshape the world to her whims, desires, and sometimes, her madness.
Here, S.W. is manipulating reality to banish Phoenix-possessed Cyclops away like a "Star Trek" matter transport machine ("Avengers vs. X-Men") :
The movieverse Scarlet Witch is a little different. First, she has no probability/reality manipulation powers. She is characterized as having "telekinesis, neuro-electric interfacing, and mental manipulation." Now, for those of us who speak in powers, this basically means she has telekinesis and telepathy. Neuro-electric interfacing is just connecting with a person's brain synapses to read their minds. Mental manipulation is her ability to hypnotize and control people's minds, which is an aspect of telepathy that most telepaths perform in the comics.
S.W.'s telekinesis is also reminiscent of Jean Grey's telekinesis. Jean is known for manifesting telekinesis that can manipulate at a molecular level, meaning that she is not just manipulating large objects, but she is also manipulating the objects' molecules, atoms, and even their subatomic particles.
Did you see the star pentagram in the second gif? Classic. I'm sure some of you have caught on by now, but you can clearly see how Cyclops and Phoenix (Jean Grey) have kind of been combined to create the movie version of Wanda Maximoff. Her powers literally are a combination of both of theirs. The reddish energy is an extension and representation of her telepathy and telekinesis. Any time she is exuding that energy, it is really her mental powers. This is VERY similar to what the Phoenix effect of Jean Grey does in the comics. However, in S.W.'s case, it is a red energy that looks very much looks like Cyclops' optic blasts. The movie version of Scarlet Witch is clearly a combination of Cyclops and Jean Grey in terms of her powers. Her telepathy and telekinesis is like Jean Grey's, and it is expressed through red energy that looks exactly like Cyclops' energy blasts.
There are probably some Marvel fans probably who wanted to see the Scarlet Witch make machines fall apart, make cloth hard as steel to turn her clothes into armor (or vice versa. Can you imagine Hulk rampaging through a bunch of Ultron robots she warped to make them like paper?), turn energy to sand, make bullets shot at her disappear, and all kinds of other probability/reality manipulations. I have to admit, though, Whedon's take on the Scarlet Witch and the way he changed her powers is kind of cool. The difference between the Avengers films and the X-Men movies is that the Avengers films show big battles similar to the "Lord of the Rings" franchise movies. I imagine it would be really hard to create really cool battle scenes where a probability manipulator can hold their own and capture the audience's attention the way scrappers like Captain America and Black Widow do. Not only that, but her powers are really hard to understand if you don't know the comics and her backstory; the movieverse doesn't really go in that direction.
However, as a telekinetic, her ripping things apart with her mind and disintegrating her enemies to atoms makes her able to hold her own in those big battles and delight and entertain Marvel fans and moviegoers alike. Am I disappointed that movieverse Scarlet Witch is nothing like the comics? Not really. I think Whedon did a really good job. It is a creative take on the Scarlet Witch and pays homage to two beloved X-Men, whether or not it was intended.