Academic medicine most generally means practicing in a place with infrastructure for research (facilities, IT, administrators, access to databases, etc) and/or teaching (associated with a medical school, ample opportunities to head services with residents on them, etc). Note you can obviously teach and be a private practice doc and you can be full-time clinical and work in an academic setting - it’s really about the institutional culture and the resources for those “extra-clinical” things that really makes the big difference (and leads to downstream differences).
Yes you can work at a big name academic place and not do research. Most docs at most academic hospitals do not conduct NIH funded research, and in my experience most really don’t publish all that much either. Also in my experience at multiple institutions, most people at academic centers align with the education mission more than the research mission. Similarly, you can do many types of research at non-academic places - you probably won’t be running cancer trials but retrospective studies, etc you likely could do (some call it being a “hobby researcher” where you’re unfounded but lead a study from time to time).
Lots of reasons pay is lower. Some include that teaching means taking time away from seeing more patients (revenue earning) and instead being with learners (not revenue earning). Often times academic places have higher overhead and administrative costs. Academic places also offer services that aren’t financially lucrative (like small subspecialties such as child metabolic clinic that don’t necessarily reimburse well at all) because they tend to be the tiertiary care centers, so they subsidize a lot of those services by borrowing from departments making more, kind of “evening out” salaries. Many more reasons than this but these are a few.
It’s obvious why researchers and educators choose academic systems, but why do many who are full-time clinical still work for academic systems vs private practice? Academic institutions handle everything (malpractice, scheduling, benefits, etc), you get to be in a very intellectual environment, often located in desirable cities, etc.