Whats the difference between current market value and fair market value on a home?

Current market value is what your appraiser and realtor says its worth. Fair market value is what its really worth.

Current Fair Market Value

The terms are basically interchangeable. The "market value" of a property is determined by what a buyer and seller agree the property is worth on the open market based on its size, location, development, etc. when neither party is under duress. If you are looking at documentation that lists these two terms for same property with different values, I would guess the source is considering duress (or supply/demand) is a factor.

Current market value means now.

Fair market value means as of whenever it is stated, like "Fair market value as of June, 2006." The word "fair" is unneccessary.

Different terms for the same value

These are terms with the same meaning, used interchangeably.

What it doesn't mean is tax appraised value, appraisal value, tax assessed value, etc..

They are the same thing...it's what someone will willingly pay in an open market.

every time i submit a question, even if its the easiest one, they cannot offer me a good informed answer . Wtf happened to people that actually make the effort to write an answer..