Both Ping and Traceroute work by sending out ping packets and waiting for replies.
Pinging your website allows you to see the latency of your website or the amount of time it takes your website's server to reply back. It also provides your website server's IP address which is useful to know whether a website is hosted on your servers or not.
Traceroute is a command which can show you the path a packet of information takes from your computer to one you specify. It will list all the routers it passes through until it reaches its destination, or fails to and is discarded. In addition to this, it will tell you how long each 'hop' from router to router takes.