A Thin Client is browser based. This means that you don't need to install any heavy stuffs and it's available across platforms and is browser based.
A Thick client on the other hand takes up back to the two tier world of client-server. This is where you install the client software on every machine that requires access to it. Mostly you also install the runtime files associated with the client.
On top of these there's a new buzz word. Rich Client. or RIA (Rich internet applications) These are one step further in prodiving rich internet (browser/thin client) based applications that perform asif you have a thick client on your machine.