"見る" and "見える"

https://hinative.com/en-US/questions/286870
[Question]
Which one is correct if I want to say "I'll watch a movie"?
映画を見る / 映画を見える

[Answer]
If you want to say "I'll watch a movie",
映画を見る is correct.
( Literal translation is "私は映画を見るつもりです。" )

In fact, the word "見る" have a very broad meaning in Japanese.
Such as: look at, watch, see, stare, think, estimate, witness, take care, read, and so on.

"見る" implicitly indicates that a subject person is bearing something in his/her mind. 
"bearing something in one's mind" causes some activity, such as "look at", "watch", "see", "think"... and so on.
It will vary depending on the situation.
Anyway, "見る" is used when you are looking at something with intention.


"見える" has different meanings. 
"seems like" その動物は猫のように見える。 The animal seems like a cat.
↑ On this case, you have no intention to consider the animal as a cat.
"can see"　ここから富士山が見える。 You can see Mt.Fuji from here.
↑ This sentence just conveys reality. It has no relation to anyone's intention.