Difference between Rule something off and Rule something out

rule something off—draw a straight line with a ruler after a piece of work:

• Rule off each exercise as you finish it.

rule something out—

1. cancel an item on a list, etc. by drawing a line through it:

• Rule out that entry in the ledger, the transaction was cancelled.

2. make smth. impossible; prevent smth.:

• The conditions of the ground ruled out any chance of hunting that day.