I think that confusion in this area might have caused quite a lot of the discussion... here goes...
Cardiac stress tests are used to study the possible presence of heart disease or its severity or extent. Raising cardiac output above the resting level is central to this. But you need to know how hard to work the patient. So a formula is used, such as 220 minus age in years predicts the maximum heart rate in beats per minute. You can then increase the exercise so that the heart rate gets to 85% (or some other fraction) of that predicted maximum heart rate. These formulae come from population studies and they won't be accurate for any particular individual, but for this purpose they're a lot better than nothing.
https://en.wikipedia.org/wiki/Heart_rat ... heart_rate
In contrast you can measure an individual's heart rate as they exercise harder and harder until it doesn't go up any more. That gives you an observed maximum heart rate for that individual for that type of exercise on that occasion.
The two values might be different for several different reasons. The formula might not be appropriate for the population from whom the individual was drawn. The individual might be unrepresentative of the population in whom the formula was determined. There will be variability in the maximum observed on a particular occasion.
I'm trying to think of a good analogy, and this might not work... but take height. It's possible to predict the height of an individual male adult in the UK without measuring the individual. 1.78 m would be a good prediction. But if you wanted to know his actual height you'd measure it. And no-one would be surprised if it wasn't 1.78 m.