In both cases, it all depends on the meat in my view/experience. IE: I have several pounds of meat in the freezer for burgers. It's bison and ground sirloin. Medium rare with both...no worries.
When it comes to ground beef, and the like, I don't want a hockey puck. But it needs to be cooked.
Again. Picky. Ground beef/Chuck? On the grill. The aforementioned, I'll do in a skillet or a number of ways.
My fifth grade teacher had my mother and I over one day for lunch. He cooked burgers, in REAL butter with onions in a cast iron skillet; covered. It's like some of the stuff I saw my grandmother do in the kitchen. It stuck with me. To this day, when I'm cooking a burger with the ground sirloin/bison? In a cast iron skillet, with REAL butter and onions, covered. (It's all about the temp here as well.)