I’m going to quibble here - Anarchists believe in anarchism, not anarchy. And anarchism as a political force predates communism by a good 60 years (when we consider Godwin vs Marx)
The central difference between libertarianism vs anarchism, IMO, is the issue of the importance of the individual vs the collective. That and the issue of private property.
A large part of winning any war is controlling what the people see and hear. If there is absolute freedom of the press in Libertania, would an outside force be allowed to buy time on the airways to make their point? Would they be allowed to own any media?
An absolute autocracy (total top-down management structure) is what is considered optimal for conducting warfare. It does not follow from that that nothing more democratic than an autocracy can ever exist because, well hell, if one ever did, then well gee whiz how would it defend itself when the autocratic regime from the next valley over comes storming in with its army?
We know that because we (most of us at any rate) live in countries far more democratic than an absolute autocracy. Many of them have a military. Those military organizations are most often considerably more autocratic than the structuring of authority in the rest of the country. Oddly enough, this has not led to a quick and immediate takeover of the country by its autocratic military, either.
One of the problems with getting people to discuss anarchy and its variants in any kind of remotely intelligent fashion is that they are predisposed to think of anarchy as being only able to exist and persist if
• all non-anarchic forms of structuring authority are FIRST destroyed
• no non-anarchic social organizations ever exist from that point onward
• everyone is always and evermore a freaking saint