Agree with #1/2; "to live for the moment" - because tomorrow I may be dead. :-)
Here's what Oxford online e.g. says:
"live for the moment
In other words, it made some people live for the future and others live for the moment.
They are the carefree ones - the dare-devils who live for the moment and leave the future to look after itself.
I'm just living for the moment, not daring to think about what the future holds."
In den Tag hinein leben - eher ein passives, planloses Sich-treiben-lassen.
That's also how I understand it, but there is some overlap in meaning.