"Prevalent" vs "prevailing"

The copy of the NOAD (New Oxford American Dictionary) installed on my Mac Mini (the computer I am using to post this answer) has the following example about the usage of prevalent and prevailing.

Wildflowers might be prevalent in the mountains during the spring months, but a particular type of wildflower might be the prevailing one.

It then adds the following explanation.

Prevalent, in other words, implies widespread occurrence or acceptance in a particular place or time (a prevalent belief during the nineteenth century), while prevailing suggests that something exists in such quantity that it surpasses or leads all others in acceptance, usage, or belief (the prevailing theory about the evolution of man).