Q:

In the distributed computing problem known as the "Byzantine fault", what differences and relations are between commander, lieutenant, and general? 

Distributed systems by Coulouris says

The Byzantine generals problem •
  In the informal statement of the Byzantine generals problem [Lamport et al.  1982], three or more generals are to agree to attack or to retreat.  One, the commander, issues the order.  The others, lieutenants to the commander, must decide whether to attack or retreat.  But one or more of the generals may be ‘treacherous’ – that is, faulty.  If the commander is treacherous, he proposes attacking to one general and retreating to another.  If a lieutenant is treacherous, he tells one of his peers that the commander told him to attack and another that they are to retreat." 

What differences and relations are between commander, lieutenant, and general? 
Can a general be either a commander or a lieutenant? 
See also https://en.wikipedia.org/wiki/Byzantine_fault

A:

In this problem statement, each general is also a commander or a lieutenant.  The commander is the general that decides for the entire group to attack.  The lieutenants are generals that are supposed to follow the commander's decision if they are reasonably sure all groups are synchronized.