<p>When I save a file with an .htm or .html extension, which one is correct and what is different?</p>

Neither is wrong, it's a matter of preference. Traditionally, MS software uses
```
htm
```
by default, and *nix prefers
```
html
```
.
As oded pointed out below, the .htm tradition was carried over from win 3.xx, where file extensions were limited to three characters.