I have 2 different bookmarks, but they take me to the same online screen.

This is most likely how the site works — you have to sign in and out between your accounts. There are ways how to stay signed into the same site with two different accounts, however they're not exactly lightweight (as it means basically running a separate browser instance with separate data), see [[Manage Firefox profiles]] for the general pattern people use. Not sure if it's worth it just for this use case though.