I guess you could run your errands running but I guess brisk walking could be easier to incorporate for most in their routine, especially for non runners. Besides, running with the wrong form could do more damage than walking.
Walking quickly (at a speed that you want to start jogging, but you don't) is less efficient for same distance than actually running..which is better for your health.
To get the same benefits from running, you need to run faster/farther than walking. Just like when you switch biking, the same 3mi loop doesn't do any good and you need to start doing 10-15mi loops instead.
Another nice thing about walking is that you can multitask to make it more stimulating, for longer. Imagine if you only went on HN and social media and Youtube while you were walking the local park.
Running a reasonable amount (contextually defined), with good form, in appropriate footwear, ideally not on hard surfaces (i.e. concrete) can be good for your joints.