Could someone tell me if there is any real difference between the two
suffuxes?
Yes and no.
No, if you mean a suffix(sic) in a URL.
Yes, if you mean a file extension to a piece of content stored in a
web server's filesystem. The difference is visible to the web server
and the web server's configuration might be (and frequently is)
different for each file type. As you say:
I know of one, which is that on my server to use server
side includes requires shtml.
The problem with this is that it introduces "coupling" (a software
design term) between the URLs to pages and their implementation. If
you want to re-implement a page that was previously static into
something more dynamic, then the URL to it would need to change and so
would all the referring links. For this reason it's now generally
considered good practice to hide this sort of detail from URLs and
keep it "under the hood".