WestJet has the worst website in the industry, bar none.
As far as I can tell, the website shows static information, while the apps do live database queries.
The website will not show reservations made with a discount code, and this thread indicates the same it apparently true for bookings made elsewhere than westjet.com. It will only show the information entered at time of booking. It will either not show reservations that have been modified, or not show the modifications.
My interactions with customer service indicate these are known issues, yet they are not considered bugs and WestJet feels it's perfectly acceptable to misinform customers.
The app may show the correct information, but it's extremely limited as well - you cannot change, or even see, seat assignments or passenger information.