I think they explain the difference very nicely, except at the end. Possibly the similarity of "variance" and "variation" makes it easy to misread the next to last sentence. Unfortunately, they skipped the details of why n is squared, trusting you to see it. The idea is that when you multiply a single random variable by 10, you are multiplying the deviation (that is, the amount by which it varies from the mean) by 10; but the variance is defined as the expectation of the square of the deviation, and therefore is squared!
Is that enough to help you out?
The other issue is that the two situations are not "both ... Var(sum of n Xs)". One is the sum of n independent random variables, and the other is a multiple of a single random variable. This is the part that they do explain well, I think.