The answers to these questions aren’t as straightforward as you would assume. Here is a study that shows some of the difficulty in making definitive statements along the lines of what you are asking.
There is, however, conventional wisdom that will maybe give you some guidelines. The folks at Polar heart monitors have a lot of this info readily available.
60-70% of max HR Good for weight loss, building endurance or recovery
70-80% " " " Good for improving cardiovascular fitness
80%+ " " " Interval workouts
if I stay in the calorie burning range, my heart won’t get noticeably stronger
It isn’t that simple. If you are very unfit, you probably won’t be able to exercise at 65% MHR for more than a few minutes, so exercising at that level will improve your cardiovascular fitness. Once you get to the point where you can comfortably stay in the 65% range for an hour, and you continue to keep your workouts in that range, then you will still be burning fat, but you’ll be maintaining your cardiovascular fitness more than improving it. To improve, you need to step it up to a higher level and this is how it goes in general. To improve strength and/or fitness, you need to challenge your body to do more. You can do this by increasing intensity and/or duration. The duration thing gets tricky in that there are diminishing returns. I’ve been doing intensity interval training for a couple of years and so I can easily stay in the 65% range all day. I’ve done 10 hr bike rides at the 65% range with only a few stops for food and bathroom breaks so increasing my duration at 65% to improve my fitness isn’t really an option.
As for the fat burning thing, it’s all about your body’s energy systems and how it gets the energy it needs to meet the challenge. ATP is the basic energy source for activity and you have three ways to make it. Aerobic glycolysis produces ATP by metabolising carbohydrates, fats and proteins. Carbs and fats are favored over proteins. It requires oxygen and so it is limited by your oxygen intake. This is why you want to stay in the 65% range where you should be breathing normally and not huffing and puffing. The Anaerobic Glycolysis/Lactic Acid System works by metabolising glycogen which is stored in the muscles and liver. It doesn’t require oxygen but it is limited by the fact that lactic acid is produced as a waste product and an overabundance of lactic acid will eventually make your muscles unable to contract. This is what is happening in exercising to failure. The ATP-PC System uses phosphocreatine (PC) to make ATP and it is limited by the amount of PC that is stored in muscle tissue.
All three systems work at the same time so you aren’t exclusively using one or the other, but in general the Aerobic system is used for low to moderate activity and the Anerobic system is used for higher intensity work with the PC system used for high intensity short bursts. This is why intensity interval training is so effective, because it improves all three systems.
If you are relatively fit, you may be able to do a few sets of weight lifting exercises and barely get your heart rate into the 65% range. So you’ll be improving your anerobic fitness and maybe your PC fitness, but you won’t be burning as much fat as if you spent all that time in the 65% zone. If you weight train hard and get your heart rate up, then after you stop lifting, your heart rate goes down and as it falls, you go back into aerobic metabolism. The more fit you are, the faster it falls but exercising at high intensity also raises your basal metabolic rate so its not a clear cut or simple formula.
I’ve really only scratched the surface of exercise pysiology, but you don’t need to know much about it to make real differences in your fitness. It all depends on what your training goals are. If you are careful about your nutrition and you exercise in the 65% range for 1/2 hr every day, you’ll look great and be fit. Consistency is way more important than anything else. Eat right and exercise regularly and you’ll do fine… but then you already knew that, eh?