They're the same because they don't quantify how much it hurts, but instead how the pain affects you.
A 10 would be pain so severe you are unable to perceive anything besides your pain or do anything except writhe.
An 8 on such a scale would be pain that makes it difficult to focus on anything else, let alone listen calmly to a person and give a coherent answer.
A 5, while being distracting, would still allow you to function on some level.
A 3 would be pain that is somewhat easy to ignore.
You see how this is a scale that can actually be measured by an outside observer and is much more useful in figuring out what medication to give. Because while two people may have the same injury, one of them may be able to completely ignore the pain even without medication - so giving medication would only do harm - while the second person may need medication in order to function.
Assuming such a scale was used, it would make sense for the nurse to say "it isn't an 8" - because if it was an eight you wouldn't have been able to listen calmly and explain that to her, by definition.