Before we go much deeper, let's answer a few questions I'm sure you have right now:

Q: Why does Boba Fett name his ships with Slave and a number?  Do they hold slaves?
A: There is no real significance of the name.  He does not carry slaves on the ships, nor does he have any slaves (Well, except droids!).  Boba Fett once said he regrets naming Slave 1 as it is.  Why? He said it's because it gives away the he has more that just Slave 1. 
Q: How many ships does Boba Fett have?
A: There are 3 known ships; Slave I, Slave II, and Slave IV. 
UPDATE 5/02 - The existance of Slave III has been confirmed.
Q: What was the ship in Episode 2?
A: It was Slave 1, at that time it was owned by Jango Fett.
Q: Why is Slave 1 colored differently in Episode 2?
A: When someone dyes their hair black, the had to have been an original color.  Slave 1 is that same way.  It originally looked like that grey, blue, and yellow color.  But it appears that Boba Fett repainted Slave 1.