Ichigo's first zanpakuto (sword) is a sword looks like a huge katana as you said. It wasn't the real zanpakuto of Ichigo, because he got it after Rukia stab him. When he fight with Byakuya (If I'm not mistaken), the Zanpakutou of him was broken by him. After trying to get the real zanpakutou of him, Ichigo finally got his real one, that is a sword looks like a giant knife like you said. Then in Soul Society, in order to defeat Byakuya and save Rukia from the execution, Ichigo learned how to use a bankai, that is a higher level of his zanpakutou; that is the last sword you mention.
The change to the bankai also increase the power of the sword and the user.
In short, the second and third sword you mentioned are the same sword. It just changed its form. However, the first sword is completely different.