The only appraisal that matters for your deal is the one that your lender will order--provided you intend to obtain financing. The only other appraisal that might matter is one that you'd order independently.
Hopefully, if you already have this property under contract, then you're represented and your contract contains an appraisal contingency. If so, then you can approach the seller to readjust your offer price, or you can opt out of the contract using your appraisal contingency. However, if your property is under contract, and your contract didn't have an appraisal contingency, then you might still have a few other options if you're represented. Yet, if your property is under contract, your contract didn't have an appraisal contingency, and you're unrepresented, then it's time for you to see an attorney to review your remaining options.
If your target property isn't currently under contract, then make sure to present your offer with an offer price no greater than the appraised value of that property.