A 100-meter sprint is a race using only the straight side of a racetrack. A 400-meter sprint is a race that makes one complete lap around a racetrack. Why are velocity and speed the same for 100-meters sprint but not a 400-m sprint?

Velocity is a vector quantity and depends on both speed and direction.

In 100m you only travel straight in one direction.

But in 400m you have to turn corners and then go back the way you came, and then turn another corner, you're changing direction - hence changing velocity, even if the speed is the same.