Watson Conversation does not use NLC. They have two very different learning models. Conversation works better with natural language classification, while NLC with text in general.
NLC also takes longer to build it's model vs Conversation. Something that will take Conversation a few minutes, can take 30 minutes or more for NLC.
Lastly NLC uses what is called relative accuracy, while Conversation uses absolute confidence.
To explain, imagine you have two intents "Cars" + "Trains".
If you ask NLC a question, it will always tell you it is car or train, even if that question is "What is an elephant?". The confidences also added together will always add up to 100%.
Conversation on the other hand can understand that your question might not be related at all to what it is trained on. So it can tell you that an elephant is not a car, nor a train.