Here is some food for thought.
If you had been using all .htm files on your website and now, for example, you have changed the editor that you are using, and your new editor is outputting all your files with the .html extension. When you re-publish your site to the server, it would seem to me that you could really hurt your SEO position/ranking as many of the links out there in the web, including Google, that were looking for the .htm and not the new .html for that same page. This assumes that you are still using the same page names from your old editor which would make sense.
Anyway... My point is, be careful not to loose that link juice you have build up. So I guess in this example, there is a reason to stick with .htm... But other then that as mentioned by everyone else they seem to be the same.
Please correct if I'm wrong.
The reason I mention all this is because this is what I was in the process of doing when it occurred to me I may be damaging the site SEO with the new editor.
The original editor was MS Front Page, which always outputted .htm, dead now, and the new editor "90 Second Web Builder 9" which outputs all .html files... Luckily, they must have thought about this and they included a way to change the output extension back to .htm
Anyway, that's my 2 cents... hope it helps someone..