before i answer, let me first say that an appraisal (by definition) simply means an opinion of value. so no two appraisers will come up with the same value. in saying that, another appraiser might ger you the value you need.
there are several ways a property gets appraised: a bpo, avm or appraisal. a bpo is a broker priced opinion, which is done by either realtors or third-party companies using tax records of sold homes to determine the value. usually a bpo costs about $150 more or less. an avm is an automated valuation model, which each servicer has to determine the property value. i don't know what values or methodoligies are used in the avm, that's behind closed doors. the third method is an actual appraisal, which can cost $300 to $400 bucks. a licensed appraiser will view the property, it's building integrity, sales of neighboring homes and other things to determine it's value. an appraiser's license is on the line so you can bet a lot of work has gone into it.
there are also different methods to appraise: using comps (neighboring homes sold); the rebuild value; or if commercial property, the amount of gross revenue generated.
if you want to refinance out of a freddie loan, you can. you can attempt an fha refi if you desire.