Assessed vs appraised vs fair market value?

OK, I'm sure someone has asked this one before. What are the general
differences between the

assessed value
appraised value and
fair market value

For a single family, residential house?

My real estate friend says there's no such thing as "fair market
value" since it's too subjective. He says fair market value is
usually tax assessed value because tax assessed value is established
by a municipality like a town or a city.

He also says that fair market value is the average price that's been
paid in the past 6 to 12 months for a house of similar specifications
and location.

So if fair market value and tax assessed value are similar, then why
is it necessary to have a property appraised to get it's appraisal
value?

How much different is appraised value versus fair market value?

Confused