The best way to differentiate the two is to look for other symptoms. Tiredness will often be lethargy accompanied by disinterest. Sickness will often have more symptoms such as vomiting, diarrhea, dizziness, and coughing. A sure-fire way to diagnose your dog is a vet visit. If things don't seem severe, you can monitor your dog for 24 and wait to see if anything improves or new symptoms arise.