There is no real difference between an HTM file and an HTML file.
Some file formats happen to have more than one option for the file ending (e.g. jpg and jpeg).
If your web server baulks at the HTM file, just change it to HTML.
Is this not linked to the fact that file extensions in Windows were (?) limited to 3 characters?
That's one factor in it.
In theory, all web servers will treat them both as web pages and serve them up without issue. But I have encountered some Microsoft IIS web servers that are set up by default to only recognise one of these file endings, and for some reason HTML seemed to be more popular than HTM. If I wanted to get Captivate content working on these servers, I had to get HTM files added by the Web Admin.
The HTM or HTML ending just indicates that the file contains HTML code. You can use either one, but it does make a difference because most web servers will regard myfile.htm and myfile.html as different files, even if they contain exactly the same code. So a hyperlink has to match exactly the file ending. If your link misses out or adds that final letter on the file ending, it could be broken.