Your loan has to pass two separate tests, and both apply at the same time.
The value test sets the ceiling. If the appraisal is 200k and the lender's maximum is 75% loan-to-value, the largest loan they'll consider is 150k. That's the most you can possibly get.
The rent test sets a second, often lower ceiling. Many rental loans use a debt service coverage ratio, which is the property's net rental income divided by the annual loan payment. A lender wanting 1.20 coverage needs rent that covers the payment 1.2 times over. If your rent only supports a payment consistent with a 130k loan, you get 130k, and the 150k the appraisal allowed is irrelevant.
Whichever test gives the smaller number is your loan. So you're screening for both from the first day, which means pulling rent comps before you make an offer rather than after the drywall is up.
The practical difference from a flip is what you're buying. A flip wants resale appeal. A rental wants a property that rents easily, holds a tenant, and doesn't generate repair calls. Those overlap but they aren't the same house. The kitchen finish that adds 12k to a resale price often adds nothing to the rent, and the roof that a flip buyer would negotiate around is a problem you'll own for a decade.
One thing to check before your next offer: coverage ratios and LTV limits vary by lender and by loan product, and some lenders also apply a minimum debt service coverage to the property regardless of your credit. Get both numbers from your actual lender in writing rather than working from a rule of thumb, since a 1.25 requirement instead of 1.20 moves your maximum loan by real money.