The second one is after the first one. (duh) Well it is a few years after Shadow Moses and Snake is back at things again but he isn't working for the government. He is work for a Anti-Metal Gear Organization called Philanthropy. They got word about a new Metal Gear in production being transported for testing. Things go way wrong and Snake gets blame for the whole mess because it is set on an Oil Tanker and it goes down. Now come the longer part of the story and a big mistake I think. You don't play as Snake you play as a guy named Raiden and I hat playin as Raiden. But the whole story is great in the end and it could lead to another Game but now the third one is set in the 60's and is the end of the series.
The guy handing the gun to the soldier is Raiden one of 2 people in the story you can play I see it as a down side to the game.
Here is Solid Snake in the tanker mission where you play as Snake but as in the pic. above I told you about Raiden and how being him for most of the sucked you play Raiden in the plant mission.(Raiden looks like a girl)
This one of the Metal Gear models in the game the amphibian model "Ray" is what you see at the start and if you didn't beat the game yet I won't ruin most of the story for yah.