I think you've mixed up relative and absolute differences. Both of your examples are in terms of absolute percentage points (pp, sometimes ambiguously labeled %), but relative changes are measured in percent (%). 300% relative difference just means 300/100 = 3x.
> Both of your examples are in terms of absolute percentage points
No, they are both about relative increases. I didn't even write about absolute increases because (unlike relative increases, where the article makes a mistake) absolute increases were the part that the article got right: a rise from 5% to 15% would be an (absolute) increase of 10% … just like the article says.
> 300% relative difference just means 300/100 = 3x
…My point was: 300% relative INCREASE (i.e. positive relative difference) means that it's the DIFFERENCE (increase) between the initial value and the end value that is 300% RELATIVE TO the initial value (thus the end value being 400% of the initial value), not that the end value is 300% of the initial value (which would only be a 200% relative increase).
Let's take, to better illustrate the point, an example with a relative increase below 100%. Let's go with an example with 40% relative increase. So let's say:
* in the reference year, your company made a profit of 5 million dollars out of a revenue of 100 million dollars, i.e. a profit margin of 5%.
* the next year it still made a revenue of 100 million dollars but managed to be more profitable, making a profit of 7 million dollars i.e. a profit margin of 7%.
* The ABSOLUTE increase of the profit margin is (7%-5%)=2%,
* The RELATIVE increase of profit margin is the absolute increase of profit margin divided by its initial reference value i.e. (7%-5%)/5% = 40%.
And my point is: having a 40% relative increase of profit margin means that your end profit margin is 40% higher relative to your initial reference profit margin and is thus (100%+40%)=140% of your initial reference profit margin, not that your end profit margin is 40% of your initial profit margin… which would be a 60% relative DECREASE (i.e. -60% relative increase) of the profit margin.