It’s a medium and communication service.
It does have a web address for site access and implementation of the service via web site.
On the other hand, Free Republic is a site. drudge Report is a site. Etc...
Twitter is a site that can be reached via SMS or a phone application that uses the subdomain site mobile.twitter.com
SMS is a communication service that allows users to communicate to a site.
Twitter is still just a site and there is nothing magickal about them.