Dear teachers, I have a problem with two definitions; the definition of the verb "die off" and that of the verb "die out". I looked them up into the dictionary but they look the same to me.

to die off: if a group of people, animals or plants die off, they die one by one until there are no more.
to die out: to stop existing.

Aren't they the same? How do you use them in English? Any example?

Thank you very much.