It is less vivid; "raced after" emits a feeling of either action, suspense, or energy. It allows the reader to connect and fully understand what is going on. "ran after" is vague and emits little high energy.
With my loyal black cat, max is the corrected error
Answer:
Wanna answer my question?
Explanation:
You know... the one I posted? Also it is going to be the second... I think
