Move is simply a change in location, which means to take something to another place.

Move指的是移动一个东西从一个位置到另一个位置。

Remove is a complete erasure from the current context, which means to get rid of something.

Remove是将一个东西从当前的环境中彻底清除掉，意思是不再需要此东西。

An example, if there was a paper posted on a bulletin board (告示栏), and you were asked to “Move it”, you would simply relocate it to a different spot on the board. If you were asked to “Remove it”, you would take it off the board completely.

Example:

I moved the file from folder A to folder B on the computer.

我操作电脑把那个文件从文件夹A挪到了文件夹B。

The tree got in the way of the villagers, so they decided to remove it.

[They either chopped(砍) it down, dug(挖) it up, burned it, or used some other method of getting it out of the way.]

一棵树挡道了村子的路，所以村民决定清除掉它。(村民会采用砍，挖，烧等方式把这棵树清理掉)

The tree got in the way of the villagers, so they decided to move it.

[They moved the tree to another spot. They dug it up and replanted it somewhere else]

一棵树挡道了村子的路，所以村民决定移动它。(移动树到其他地方)