Adjusted Book Value takes true fair market value of all assets and liabilities into account. Adjusted Book Value tends to be used when a company has been devalued to the point of facing possible bankruptcy and liquidation.
Book value in general does not account for intangible assets, such as intellectual property, so it is more useful in assessing the risk of loss in a foundering company than the earnings potential of a profitable company. Technically the adjustments to book value will raise or lower the value of assets and liabilities according to current fair market value.
Fair market value is the replacement value or salvage value of an asset. It can be appropriate for valuation of real estate holding companies and investment companies, both of which are mostly constituted by the fair market value of their assets.
Revenue Ruling 59-60 actually states that earnings valuations, and not adjusted book value, is the preferred method to value companies who are anticipated to be liquidated.