Yes you could analyze how each works & with a little practise easily determine their working.
Actually by studying packets you can even identify problems in your internal network.
Let me warn you though,there arent just ping,tracert commands & their output to learn there are a large number of protocols & metrics
I had my internal lab network all haywire at the time of writing so consider this for an example
Pinging a site such as
www.oobertech.net yields captures taken from Ethereal
The above shows a lot of information about which source port,destination port,Type of Frame,Type of protocol & most importantly replies to the each ping query.Although the capture was w.r.t internet activity,it can be used to solve & understand problems related to the internal network.
To sum it all up it can reveal a wealth of information.I dont have a hands-on experience with Packetmon,but Ethereal is one helluva analyzer to have in your toolkit.