yes, the main distinguish here is the word "application". I believe that these days most web hosting plans support "applications". Both choices are available for MVC. I mean, if you looking to post up say some test pages, or a sub-site to a EXISTING hosted site, then web site is better.
So the two choices are: asp.net web site
and
Asp.net web site application.
web site "application" quite much assumes that the whole site and whole application is going to be the web site.
And another notable difference is that a web site allows you to copy "one" page, and update code for one page and not have to re-deploy the whole site.
With a web site application, while the web pages are published, the code is not, and all dependences and code is pre-compiled.
The difference is explained here:
dd547590(v=vs.110)
I probably should not even noted or mentioned this difference, but you are MUCH better to use a web site application, and everything suggests that's what you done now anyway.
So, my comments about using a web site vs web site application probably don't apply. It can be more difficult to publish a web site application as a "sub folder" or site to a existing site, but that does not look to be a issue for you. Most plans that support asp.net should work and be just fine for your use.