The gap between two values as a percentage of their average — symmetric, so the order you type them in does not change the answer.
Result
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Percentage change has a direction and a starting point. From 40 to 44 is a 10% increase; from 44 to 40 is a 9.09% decrease. The two numbers differ because the denominator is where you started, and that swaps when you reverse the order.
Percentage difference has neither. Between 40 and 44 it is 9.52%, and between 44 and 40 it is 9.52% as well, because the denominator is the average of the two: the gap of 4 divided by 42, times 100. Symmetry is the whole point.
Which to use depends on whether one value came from the other. A price that rose from 40 to 44 changed by 10% — there is a before and an after. Two quotes for the same job, at 40 and 44, differ by 9.52% — neither is the reference, and asking "how much did it rise" is the wrong question. Reaching for change where difference belongs is the mistake this page exists to prevent.
Subtract one from the other, divide by their average, and multiply by 100. For 40 and 44 the gap is 4, the average is 42, and 4 divided by 42 times 100 is 9.52%. Dividing by 42 rather than by 40 is what makes the result independent of the order.
Use difference when the two values are simultaneous and neither is a baseline — two quotes, two measurements of the same experiment, the same product in two shops. Use change when one value became the other over time.
Yes. Between 10 and 100 the average is 55, so the difference is 163.6%. That is ordinary whenever the two values are far apart, and a calculator that stops at 100% has confused this with a share of a whole.
Add, subtract, multiply and divide fractions — exactly, never rounded.
Solve a proportion — with the inverse case the usual formula gets wrong.
What is X% of Y — the everyday percentage, worked out step by step.
Add a percentage to a value, or find the increase between two numbers.
The price after a discount — and the price before it, from the sale tag.
The tip, the total and what each person owes — including the cent that does not divide.