What is the difference between NADA and Kelly Blue Book; i.e. why
would an estimated car value be substantially different between the
two (NADA higher by ~ $2K)?

Two different opinions.

Each online vehicle value source takes different variables into
consideration, such as geography, market conditions, supply and
demand, etc. Some are updated more frequently than others. None are
able to provide an exact value or appraisal amount because they do not
physically inspect each vehicle. Values are solely based on user input
(which can be manipulated by buyer or seller) and whatever criteria
they deem relevant (varies from source to source). These services
provide estimates only and not meant to replace a physical appraisal
of your vehicle, but they have become a very popular proxy source for
vehicle value data online.

A good place to look for a free, no-obligation physical appraisals is
a CarMax store (www.carmax.com) or any appraisers accredited by a
reputable national organization.