Ping is used to see if a specific host is connected to the internet. Ping works by sending a packet of info to a host. If the host is connected and functioning properly, it will send the info back. Ping will also display how long it took, if the IP address was invalid, or if there was no response. Ping can also be used to see if the TCP/IP software is working on a computer.
Traceroute is used to figure out if there was any problems with the performance of large networks. Traceroute will collect data of the packets path from source to destination, and how many times it had to hop to get to its destination.