Your definition applies to both recklessness and negligence. But there is a legal difference between the two.
"A person acts recklessly, or is reckless, with respect to circumstances surrounding his conduct or the result of his conduct when he is aware of but consciously disregards a substantial and unjustifiable risk that the circumstances exist or the result will occur."
This would mean the prosecution would have to prove that Guyger was "aware" of the risk or that she could end up shooting an innocent person, but did it anyway. If Guyger was not aware of the circumstances, she wasn't reckless.
"A person acts with criminal negligence, or is criminally negligent, with respect to circumstances surrounding his conduct or the result of his conduct when he ought to be aware of a substantial and unjustifiable risk that the circumstances exist or the result will occur."
The only difference in the definition is between "is" and "ought to be". The prosecution would only have to argue that Guyger should have been aware that by walking around with a gun at the ready while completely exhausted and not paying attention to anything that she was creating a substantial and unjustifiable risk that she could kill an innocent person.