Stamp Identification Help

Hey folks, I'm home for the weekend and I had stamp albums waiting! So now I'm putting stamps in :]

I'm wondering how to discern some differences between stamps are the same, but have slight variation.

For example, I am putting in 2001 Statue of Liberty stamps now, and it has 'coil' 'coil, round corners' 'coil, square corners' 'booklet'
How can I tell these differences from individual stamps?

What does die cut mean? Is that something I can see on an individual stamp?

Thanks!