The first, and one I focus on the least, is what I call RUNNING NEXT TO THE BALL. This is when you are dribbling into space and take larger touches into space. Often times, a player takes a touch every 3-4 steps. I think this is honestly the most common type of dribbling that players are comfortable doing.
The second, is what I call RUNNING WITH THE BALL. This form of dribbling is also into space, but where you are taking a touch every step. This is what Cristiano Ronaldo is most commonly seen doing. The focus on taking a touch every touch allows a player to stop or change direction on a dime.
The third, most vital, and least focused on type is DRIBBLING UNDER PRESSURE TO EITHER POSSESS OR PENETRATE. This is used when taking on multiple players in tight spaces where you are trying to MOVE or beat an opponent. The key words there was "MOVE an opponent". Too often, we teach dribbling as beating an opponent to get behind them. What we need to focus on more is the ability to move an opponent to set up a passing, crossing, or shooting avenue. I also considering the ability to properly shield a ball to kill a game off is also this skill. I've lost my love affair with stressing 1v1s and have focused primarily on building confidence with being able to keep possession of the ball with 2 defenders trying to steal the ball from you. The reason its beneficial to work against 2 defenders is because often times, players push the ball too far after beating the first defender, so I always teach to dribble while having the SECOND defender in mind.
So next time you're focusing on dribbling, determine which one you want to work on, and always have the second defender in mind!