Speed and Agility are terms commonly used interchangeably but they mean very different things. Linear speed refers to the top speed a person can achieve (think track sprinting events). Agility refers to how quickly someone can accelerate, decelerate and re-accelerate off in a new direction (think making a cut in football).
Tennis definitely falls into the category of being a sport where agility is more important than linear speed. Players need to be able to be changing directions often and quickly to reach higher levels. The most important aspect to being quick is the first step a player takes. The first step absolutely has to be explosive and aggressive. I use this analogy to teach kids about the importance of the first acceleration step:
Imagine have a race against someone for 10 yards. Who wins the person with the highest top speed or the person who gets off the starting line fastest? It is always the one who gets off the line faster. Tennis is the same way, a player is in a short distance race with the ball. If they beat the ball there they are in good shape, if they get there at the same time as the ball it is much harder, and if the ball beats them there the point is over.
I do all kinds of explosive first step and agility drills during on court training. Here is a video of two kids who were training together just the other day. I put them in red bands at their hips. This created an overload where they had to explode through the band on the first step to overcome the resistance. We then would take off the resistance and go back to the court for drilling. I can tell you the first step was quick in this lesson!