What is the difference between NFPA and NEC?

NFPA is the organization; the NEC is one of its publications. The National Fire Protection Association publishes hundreds of standards, and the National Electrical Code is officially NFPA 70.

NFPA 70E is a different document: workplace electrical safety, arc flash boundaries, and lockout practices. The NEC says how to build the installation; 70E says how to work on it without getting hurt.

The NEC is not automatically law. It becomes enforceable when a state or city adopts it, often with amendments and often a cycle or two behind the newest edition.

So electricians care about the NEC because their inspector enforces a specific adopted edition of it, amendments included.

The NEC wire size tool keeps the code's tables at hand with the article cited on every result.