Take a 30 year old man, 75 kilograms and 175 centimetres. The Mifflin-St Jeor equation puts his resting metabolic rate at 1,699 calories a day. The older Harris-Benedict equation puts it at 1,763. Neither is wrong. They are different curves fitted to different groups of people.
Where the bigger uncertainty enters
Resting rate is the part these formulas estimate reasonably well. The larger number, total daily energy expenditure, is that resting figure multiplied by an activity factor you select from a short list of descriptions.
For the same person, an activity factor of 1.55 gives 2,633 calories a day. The steps between the listed activity levels are far larger than the 64 calorie gap between the two resting equations, and choosing between "moderately active" and "very active" is a subjective judgement about a week you have not had yet.
Why the individual variation is larger still
Two people matching on age, sex, height and weight can differ in resting expenditure by a couple of hundred calories, because the equations cannot see body composition, thyroid function, medication, sleep or how much someone fidgets. Muscle costs more to maintain than fat, and the inputs contain no way to distinguish them.
This is the same limitation that makes BMI a screening figure rather than a measurement. A formula built from height and weight cannot know what the weight is made of.
How to use an estimate that has error bars
The number is most useful as a starting point to be corrected against reality. Eat at the estimate for a fortnight, track weight across the whole period rather than day to day, and adjust based on what actually happened. That feedback loop is more reliable than any equation, because it is measuring you rather than a population average.
Day-to-day weight is mostly water, glycogen and gut contents. A three day trend says almost nothing; a three week trend says a great deal.
What the deficit figure means
For the same person, a target of half a kilogram a week works out at 2,083 calories a day, a deficit of 550 calories, which is about 21 per cent below maintenance. Larger deficits are harder to sustain and cost more lean mass, and gradual change is the framing worth keeping.
The BMR calculator shows both equations side by side, the TDEE calculator adds the activity multiplier, and the calorie deficit calculator converts a target rate of change into a daily figure. For anything involving a medical condition, the honest answer is a doctor or dietitian rather than any of them.