Hiking is walking in nature on trails or other non-road surfaces. The most accessible form is day hiking: a trip you finish in one day, usually with a light pack for water, snacks, and essentials.
Backpacking is a multi-day form of hiking where you carry everything you need to stay overnight in the wilderness—typically a larger specialized pack with shelter, a sleeping system, food for the trip, and other gear for more than 24 hours outdoors. Trips can last one night or many months (including thru-hikes on long trails).
In short: hiking is the broader activity of trail walking; backpacking adds overnight self-sufficiency and the gear that requires.
Source: Hiking for Beginners: The Essential Guide — American Hiking Society