What is meant by value, full value, fair market value, or full market value?

They all have the same meaning for assessment purposes. It is simply defined as the price a willing buyer would pay a willing seller in an arm length transaction.

The International Association of Assessing Officers defines a property assessment valuation as “The most probable price, expressed in terms of money, that a property would bring if exposed for sale in the open market in an arm's-length transaction between a willing seller and a willing buyer, both of whom are knowledgeable concerning all the uses to which it is adapted and for which it is capable of being used.”