Why is it that I can PING a site even when it's not responding to my Web browser?

Sometimes when I go on this cool adoptables site called Squiby, it says "Cannot connect to the server" or "The server is taking too long to respond". Yet when I open the command prompt and ping it, it responds in mere milliseconds. What's up with that? Doesn't "taking too long to respond" after waiting and waiting, mean the *server* shouldn't be responding?