There are two separate Apple ID logins on each iOS device.

The main one is for iCloud and other user account specific stuff. This login is set in the iCloud section of Settings.

A separate Apple ID login is used for the Apple Store. It sounds like your iPad has your wife's Apple ID set for the Apple Store. Scroll down in the Settings list until you find the iTunes and App Store section.

It is common for a family to have individual logins for iCloud on each device but share a common iTunes and App Store login for app and content purchases.

It is also possible to change the App Store login, purchase an app, then change the App Store to another Apple ID and purchase something else. This all works except when it comes time to Update, only the apps purchased with the currently logged in Apple ID can be updated.

So if you and your wife have each been purchasing apps on the same iPad but using different Apple ID then some updates won't work until you change the iTunes and App Store login. *

* This is my current understanding, going from memory.