What you have is the difference between the assess value for taxes and the fair market value (real value) of the property.
The assessed value is what the property taxes on your home will be calculated on, even if the market value is much higher. Understanding the difference between these types of value is important, especially if you will be buying or building a home and need a lender for a mortgage. It is also important to note that often the market value of a home does not conform to the assessed value of the same home.
Assessed value is the value of a property as of a certain date (usually January 1st) according to the tax rolls of your local
government jurisdiction (county or city). This value can be higher or lower than market value based on the assessment
ratio, which is a percentage of market value.
Market value is the most probable price as of a specific date (the date of sale) that a property with all its rights should sell after reasonable exposure to buyers in a competitive market with the sellers under no undue duress (meaning the sellers aren't forced to sell).
Loan applications are part of the mortgage process, and the lender will compare the assessed value vs market value of the home. For the lender, the market value of the home is the most important of these two amounts, because this is the amount that the lender will use to value the home.
Yes you still have a case to try and lower your taxes. You should look at the county records for similar homes in your area and see if the assessed value is higher or lower than yours. If you have a house that is just like yours and you have a higher assessed value then you have a case that your assessed value is too high. Most county's have this information on comparable properties available online for you to review.
Let me know if you have any questions.