what is the difference between a hot and a cold wallet?
A hot wallet is something, where the funds are stored on a wallet, which is connected to the network, and holds a small amount of bitcoins. This allows instant withdrawls.
A cold wallet is a wallet not connected to the network, and secures the coins from hacking/ flaw on the site, which might allow users to withdraw all the funds. The cold wallet is offline, and holds the majority of the coins.
Hot wallet usually means it's actually a full node on the webserver, that contains the wallet.dat files with the private keys.
There is also the middle wallet or online wallet, but can be reasonably secured, on a different computer that is not the website. Maybe it's a home computer of the owner, or some special purpose laptop in the office or something.
Cold wallet is generally offline. There is a watch-only wallet on the servers, or you can just check in the block chain.