While there is no standard definition, this may help:
Historically, a web site was a page on the world-wide-web that served content. Links where nearly the only way of interacting with each page, simply navigating you to another page.
Regardless, a site can only be accessed via a browser. Apps likes the Apple store, Spotify or BBC sport (which are alleged to be technologically site-based with a browser wrapped within an app) are still apps.
Content vs Tasks
In search to classify something as a site or an app, you can argue that sites are more content based (much more time spent on user input than user output), whereas apps are more task, or interaction based.
View state vs Business state
Deep within UX modelling you can distinguish between two classes of user actions:
- Those meant to alter the view (like a collapse button). In general, the view state is not persisted (saved), although there are many exceptions to this (cookies or user view settings).
- Those meant to alter some persisted business state that is part of fulfilling a user task (and thus - a goal). In most cases, the state being manipulated belongs to the user and isn't shared with everyone on the web (there must be a login and the user state is not all public).
Using these definitions, Wikipedia, BBC, and Coursera are all sites (so long accessed from a browser). The Ghost blog, Google Docs, or an accounting software are apps.
Even with these definitions you'll find edge cases and hybrids that don't quite fall into one category or another. Arguably, Facebook, Pintrest and Stackexchange are more sites, but mainly as the state being manipulated is shared and not part of a some business goal (even for individuals).
What to call it?
I have no idea what your product is about and how does it map to the definitions above. But if it does involve a private manipulation of a private business state as part of a user task, you may wish to call it an online/mobile app.