Walking long-ish distances makes me more sore than running the same distance

I run 3 days a week and walk 3 days. Once a week I do a long run of 12-15 miles (2 - 2.5 hours), and my legs aren't sore at all. But on my once a week 12-15 mile walk (3 - 4 hours) my legs get sore/stiff by the end.

I can walk 10 miles with no soreness. It's longer than that when my legs start to object. I'd like to sometimes make my long walks about 20 miles, but as of now I can't.

Do y'all have any suggestions about addressing soreness as it arises and then continuing on?

(And I apologize for using miles instead of steps. I hope that doesn't violate some rule, as I can see that y'all are into steps. Millions of steps.)