My NJ return is asking for partnership income. Is this referring to my single person LLC?

It depends.  

If you only have a single-member LLC on your federal return, then no, your state return is not asking about this when it refers to partnership income.  New Jersey treats single-member LLC income in the same manner as your federal return.  Therefore, it would be reported on your personal return as a business.  

If you have a Schedule K-1 from a partnership, then that would be what your New Jersey return is referring to when asking about your partnership income as this would prompt a different set of questions within the New Jersey state interview.

Please see where do I enter a Schedule K-1 that I received to review your federal input and confirm whether you still have entries for a Schedule K-1 from a partnership.