Can't answer for Finland, but in Norway:
>Does that include their "offshore" income?
Yes. It counts as taxable income even if you end up paying 0% tax on it (such as via foreign tax credit).
>Also, what is income?
Net realized income. You can't tell the difference between earning $1M, and earning $10M and losing $9M, and earning $10M on paper but only selling $1M.