Meaning: This sentence describes a dog moving rapidly by using its legs.
Choice of Words: Dogs are known for their running abilities, and "quickly" means at a fast pace.
Meaning: This means that all dogs generally move fast on foot.
Choice of Words: We changed "the dog" to "dogs" to talk about all dogs in general. "Run" is still the verb that means to move fast on foot.
Meaning: This means that the specific dog is currently moving fast on foot.
Choice of Words: We changed "runs" to "is running" to show that the dog is currently in the action of moving fast on foot.