Both metrics are useful because they isolate different parts of the investment.
Cap rate
Cap rate is generally NOI divided by property value or purchase price. A property producing $10,000 in NOI at a $125,000 purchase price has an 8% cap rate.
Cash-on-cash return
Cash-on-cash return uses annual pre-tax cash flow after debt service divided by the cash invested. If an investor puts $30,000 into a deal and receives $3,000 of annual cash flow, the cash-on-cash return is 10%.
Why they can move in opposite directions
More leverage can raise cash-on-cash returns because less cash is invested, but it does not improve the property's NOI or cap rate. It also increases debt service and downside risk.
Use both: Cap rate helps evaluate the property. Cash-on-cash return helps evaluate the property plus the financing structure.