It sounds pretty much the same, but is distinctly different. That's where much of the confusion in the popular press comes from. The difference is that, as hig

It sounds pretty much the same, but is distinctly different. That's where much of the confusion in the popular press comes from. The difference is that, as highlighted in your quote, there is some null hypothesis that is assumed when discussing p-values. For example: what is the probability of drawing x>2 when the underlying distribution is assumed to be a standard normal distribution N(0,1)? The probability is small in this case, and could provide evidence to reject the null hypothesis (i.e. the distribution is not standard normal). It doesn't tell you about the probability of drawing x>2, it only gives evidence to reject (or not) the null hypothesis. The wiki has more elaborate explanation. And probably better examples than mine.