i think of hiking as something done over uneven ground, maybe a dirt trail at most. a "walk" is a broader term, but is tended to be associated as a means of travel ("take a" bus, car, bike, walk) over a paved surface in the context of the built environment.
i don't assume this is technically correct, but if i am trying to talk plainly that's how i use them. confusing or blurring the boundaries can be an easy bit, because hike implies more distance and maybe even gear. "the bathroom is downstairs. it's kind of a hike."
also there's the dismissive go away... "take a walk, buddy" vs "take a hike, buddy"... the hike one seems to tell someone to go farther away, maybe in a direction away from other people even."
I'd say this is accurate, it's mostly how well-groomed the path is. A hike will require you to navigate over natural obstacles like rocks, roots, logs, streams, etc. at some point, where a walk does not. A paved path all the way up a mountain is a walk, but a relatively flat but rocky trail through the woods is a hike.