Is this a run-on sentence?
When a dog wags its tail, it doesn't always mean the dog is happy or friendly, a wag that is slow and restrained may convey a warning to "back off."

 - yes
 - no
This is a run-on sentence. It is a comma splice formed from two sentences run together, joined by just a comma.
When a dog wags its tail, it doesn't always mean the dog is happy or friendly, a wag that is slow and restrained may convey a warning to "back off."
Here is one way to fix the run-on sentence:
When a dog wags its tail, it doesn't always mean the dog is happy or friendly. A wag that is slow and restrained may convey a warning to "back off."