Oh, no. Thucydides, these are great questions. And I hope it's okay; I love to talk about it. The old notation (pre-1950s) used a descriptive notation:
1. King's Knight to King's Knight Three
1. ... King's Pawn to King's Pawn Four
You can see the confusion and smell the many fallen trees in the grand name of long chess books.
Bobby Fischer was an amazing person in that he, and those who followed him, really changed the way piece notation was written. The first name of the piece comes before the square it moves to. For instance, Nc3. A knight that can move to c3 moves to that square. Where the piece comes from is not as important as where it goes because 95% of the time it resolves itself. Only pawn, knights, and rooks have a chance for going to one square from a differing starting point. Sometimes you need a little more, so you give a square designation to the peace. If both knights can go to c3, you say which file it comes from:
Nbc3 or
Ncc3
Either the knight on file b or the knight on file c went to the square c3.
If that's still confusing, you number the square instead. If a knight on the a-file (one knight on a2 and one knight on a4) moves to c3:
N2c3 or
N4c3
Pawns are different. You don't have to say the name of a moving pawn (though some do, it's just assumed). e4 for instance
e4
(the e-file pawn moved to the e4 square)
If a pawn captures...
You know I'd rather clarify these as we go. If I had a board to put in front of you and I could show you, I know you'd see it as very simple because you're *very* good at this diplomacy game.
Also, I can write an encyclopedia on chess strategy and history, and, again, I LOVE to talk about it. So if you have any questions, please ask.
I hope I haven't scared you away. :-)