That's easy. With a ping you can only send packets to your destination. With extended ping you can not only choose the destination but also the source , packet size, no. Of repeats . This can be very useful. Extended ping still uses ping but it allows you to manipulate it more granularly.
BTW, earlier IOS versions didn't support any options with the non-extended (command line) ping. Later IOS versions support several options with the non-extended (command line) ping (as Dennis notes), but more options are still available if you use the extended (prompted) ping command.
Well, basically it (ping and extended ping)has the same purpose and the same definition, ping is useful to diagnostic or verify if a host or interface is reachable sending an ICMP (Internet Control Message protocol). Usually ping works as reciprocal (2 ways), so if a source send a request to a destination, the destination must send a response to the source, otherwise the ping is unsuccessful.
Usually when ping is executed it send 4 packets, with extended ping it can keep a ping for an undefined time (permanent).
On Cisco devices you can add other parameters to the ping, like packet size, repeat, source, etc.
Hope it is useful