Currently, it looks like the site and the app are showing the same thing. Admittedly, I haven't done a lot of comparisons between them before, but maybe it's a caching issue??
The app is, by far, the easiest way to check, though. I hate the way the calendars work on the site, particularly if you are trying to check into the next month - choose the park, then choose the month. Want to check another park? You have to do the same process - choose the park, then choose the month.