The schools that are highly ranked on the research side get a lot of grant funding from NSF, NIH, etc. They have academic medicine faculty that do cutting-edge research (as the name of the ranking implies.) As you'll notice from the actual list of schools on this ranking, most of the "big name" schools are "big name" because of research funding. (One of the major factors US News usues to make this ranking is the grant money coming into the school: 30% of the ranking comes from this figure.) So, when you say, "I want to go to Mayo" (for example), people have heard of the school and are impressed because it is highly ranked, and it is highly ranked because it gets a lot of funding and does a lot of research, which of course means there are a lot of really smart folks there. Make sense?
On the flip side, the Primary Care ranking is concerned with medical schools' focus on providing care to patients. If you read the "Methodology" section in US News about the rankings, it says that 30% of the Primary Care ranking is based on the number of grads from that school going into primary care specialties (family practice, pediatrics, and internal medicine.) In both rankings, there is a nebulous "quality assessment" score that accounts for 40% of the ranking and is the same for both research and primary care rankings.
I guess the point is, if you're interested in primary care (which, if you want to be a plastic surgeon, you probably aren't) then focus more on that ranking; if you want everyone to be impressed when you tell them where you went to med school, then focus on the research ranking. 😉 Of course, there are many schools that are ranked on both, so if you want a mix of both, then look at those. Hope this helps!