Under what scenario should I select the adjustment tax return and claim process?

You can pick the Adjustment process when you correct underreported amounts or overreported amounts.
If you owe tax
Pay the amount due by the time you file file Form 941-X.
If you have a credit
You overreported employment taxes and want the IRS to apply the credit to Form 941 or Form 944 for the period during which you filed Form 941-X.

The claim process can be used when you’re correcting overreported amounts only and claiming a refund or abatement for the credit.