Only the address "subdomain.example.com" is a true subdomain. The address "example.com/subdomain" is a directory (or as some people say, subdirectory.) A server can be configured so the it points requests for the subdomain address to the content in a directory, and this can cause some confusion about naming - however, the two are different.
If the same content can be accessed directly with either form of address, it can create "duplicate" problems with search engine indexing, so it's good to be clear, choose just one form for your content, and permanently redirect (301 status) the other address to your prefered form of the url.
Yeah, I did more research right after and realized the latter example wasn't a subdomain at all. My bad!
Thanks for the tip. I think I'll use the subdirectory since all the articles I've read basically state that people are easily confused... well, that they don't know if they should use "www" before the subdomain.