Speed can be used as a verb meaning "to move quickly". So, I can say:
"He drove down the highway."
"He sped down the highway."
And they both mean pretty much the same thing.
HOWEVER, does that mean the two words are synonymous? Not so fast!
First of all, drive (or drove) works well with automobiles, but speed (or sped) could work with other vehicles, such as airplanes:
The jet sped across the flight deck of the aircraft carrier.
The steamboat sped down the river.
(I would not use the verb drove in those sentences.)
The verb speed can also be used for people or animals:
The referee sped across the field to break up the fight.
The cheetah sped toward the water hole where the zebras were drinking.
Also, when talking about automobiles, drive can be used refer to a leisurely, unhurried speed.
Linda and Max drove out to the park on Sunday.
(I would not use sped in that sentence, unless they were driving fast.)
Lastly, when it comes to driving a car, the word speeding is used to mean you are exceeding the posted speed limit. So:
The red Porsche sped through the red light.
might imply that, not only did the car go through the red light, but it did so by exceeding the speed limit. So, when applying the verb speed to someone's driving, it might mean "drive quickly," or, in the eyes of the law, it might also mean "drive too quickly." The meaning can be a little blurry, and, without additional context, there might be some ambiguity.