Can I use two different Apple IDs?

NotePlan syncs primarily with Apple's CloudKit, which is part of iCloud. For this reason you need to use the same Apple ID across devices. You can't change the iCloud Apple ID login for a specific app, you will need to login in the iOS/macOS system settings using the same Apple ID as on your other devices. 

One workaround is to use the web version, this allows you to use a different Apple ID than the one you are using on your system: Web Version.