Is 30 minutes to nine the same as 30 minutes after 8 in life

Yes it is the same because 30 minutes before 9 is 8:30 and 30 minutes after 8 is 8:30

Yes. In real life, those are both the same time.

If somebody said she'll meet you on the corner at 30 minutes to nine,

and you arrived there at 30 minutes after eight, then you both arrived

on the corner at exactly the same time. In real life.