This is a Hollywood-type confusion, very frequent.
A catastrophic event, as the one clearly meant in the summary, is one where lots of people die, technology is damaged (ie, electric infrastructure is busted, telecomm stops working, etc.) and life as we know it is no more, but life goes on.
Apocalypse is an event of biblical origin (apocalypse is the last book of the Bible, meaning "revelation"), and it explains the end of the world, that is, the end of life as we know it, and the world as we know it, and humans in general as we know them. Apocalypse will be a time when the dead will live again, with different qualities, and Earth will be renewed.
So talking of "life after apocalypse" is a confusion of terms. It would be a lot more proper to talk of "life after a catastrophic event".
It usually churns my stomach -as a Christian- to watch movies like 2012, where we have an "apocalypse" (catastrophic event falsely linked to the biblical event) just to find out that now we have a broken up, backwards world, ruled by some advantageous morons, and inhabited by egotistical ciizens. My, what a world!
To keep things clear, the main event of the biblical apocalypse is the second coming of Jesus Christ, to renew everything and rule an eternal life of complete happiness. And, if you are not christian, or believer, if you are a person (a lot of them here on
Apocalypse will invove a catastrophic event, no doubt, but things afterward will be a lot different.