Can entries in a form in App A populate answers in a form in App B based on given criteria.

Yes if you use an automation and depends what your criteria is.

I tried to edit my post to finish explaining but it errored out and didn't save. So my thought is that if the user in App A completes her form and posts to her table and the set criteria initiates an automation that sends that information to App B and populates the table will the table treat her entries the same way it does for information submitted via its actual form? In the actual form the options are built in through table to table relationships and there are selection dependent dropdowns. As long as her entries are identical to the options on the form will it adopt them in the same format?

I'm probably overthinking it.