Divergence
Divergence refers to momentum that moves in the direction opposite to the direction of the price trend. Divergence also refers to momentum higher or lower, but less high or low than a previous peak or trough, while the price trend is making a new higher high or lower low. Technically, they’re both going in the same direction, so it;s a misnomer to call it a divergence, but when momentum falls proportionately short of the price move, you can think of it as a failure to confirm.
Source: Rockefeller, Barbara. Technical Analysis for Dummies; (c) 2004.
Confirmation
In a pattern, it is the point at which a stock or commodity exits an Area Pattern in the expected direction by an amount of price and volume sufficient to meet minimum pattern requirements for a bona fide breakout. In the Dow Theory, it means both the Industrial Average and the Transportation Average have registered new highs or lows during the same advance or decline. If only one of the Averages establishes a new high (or low) and the other one does not, it would be a nonconfirmation, or Divergence. This is also true of oscillators. To confirm a new high (or low) in a stock or commodity, an oscillator needs to reach a new high (or low) as well.
Failure of the oscillator to confirm a new high (or low) is called a Divergence and would be considered an early indication of a potential Reversal in direction.
Source: Edwards, Robert and Magee, John. Technical Analysis of Stock Trends 9th Edition; (c) 2007.