Why your app shows a different number
Free consumer apps usually display a VantageScore or a general purpose FICO. Mortgage underwriting uses older, mortgage specific FICO models that weight certain items differently.
A gap of twenty to forty points between an app and a mortgage pull is common and does not mean anything is wrong. Treat the app as a trend line, not a verdict.
How the score is selected
Three bureaus produce three scores. Your qualifying score is the middle one. If you apply with someone else, the qualifying score is the lower of your two middle scores.
That single rule explains a great deal. Sometimes the strongest move is applying with one borrower rather than two, and sometimes it is spending sixty days repairing one report.