Fair value and Market value

What is the difference between fair value and market value?

What i understand is that fair value is actually the market value but it could be different because it is price agreed between the seller and buyer and either the buyer negotiated the price which means it is going to be lower than the market value or seller has convinced the buyer to pay more for the asset than it actual market price?

For example the seller is ready to sell the asset for $100,000 but the buyer negotiated the price and seller agreed to accept $90,000 even though the marker price of the assets was $100,000?

Another scenario is that the seller has convinced the buyer for the potential benefits of the asset and buyer is willing to pay more for the asset to $120,000 even though the actual market price is $100,000?

Please correct me.