Why they are not the same
There are a lot of negative opinions of anarchy that I've often heard phrased as follows:
Anarchists "can't get anything done." They don't organize because "they don't believe in hierarchy." They don't have anyone in charge because everyone is in charge, or there's no such thing as being in charge, "so there is no direction." 
An important takeaway here is the assumption made about organization, about structure: that it is inherently hierarchical.
This is false.
Organization can exist quite separately from hierarchy. Especially with the right amount of communication.
Organization enables us to have individual voices within a community setting. It helps us speak up to shape the world we want to live in.
Without this organization, this structure, we fall back on the old patterns we so despise; ones dominated by racist, patriarchal, sexist, capitalist elements.
Notice, in reading these guides, that this can happen without hierarchy. This is possible because the organization, like any living thing, is organic. It allows room for growth, for individual voices to join and shape its outcome.
You'd be right in thinking that there is a lot of communication happening. You might feel like nothing is getting done because all you're doing is talking.
For some, this really is a drawback, but it pays off in the end, since it ensures a sense of respect and solidarity among members of the community. If everyone feels like they're heard, then they are more likely to contribute positively to the group in the future.
Dean Spade's Mutual Aid goes into this as well: organizing is key to any successful movement, and does not have to have an element of toxic power dynamics.
He also writes about this on his blog. The post here is about organizational dynamics for existing groups.
Though the post is before the COVID-19 pandemic and the topic itself is more developed in his book - with a more focused call to dismantle our capitalist society - it is a great introduction to looking at how organizational dynamics is like now versus what it could be: ridding of hierarchies but still considering the needs and goals of the group as a whole.
Spade also introduces the decision-making system I mentioned above, called "consensus decision-making". There's a flow chart for this in the book as well, which I could not find online, but it is on page 79 of the print copy.
The next example is more anecdotal. I currently am a potential member of an anarchist tech workers' co-op. Everyone has different specialties, but everyone gets paid the same hourly rate, and no specialty gives you more say in the group than someone with different skills. The co-op opted for a non-hierarchical format.
That said, we also have values in this co-op. Those values are on our website and we take them seriously.
Additionally, each client has unique needs that we incorporate into the smaller groups working on those projects. When their needs require a smaller group to switch their priorities, we draft a letter signed from each person participating, outlining how our time commitments to other projects will change as well as when that priority period will conclude.
This probably looks similar to what you might do in a "typical company" - letting people in your group know when priorities are shifting and updating your availability as a result.
That's because anarchic groups still have organization; we have processes in place. Just because we're opting to do away with hierarchy, doesn't mean we aren't thinking ahead, leaving other people in our group high and dry when something urgent or unexpected comes along.
We also had a conversation the other day about how to respond when someone might not make it to meetings on a regular basis.
What does that "escalation" process look like?
Do we want to make it seem that important where individuals feel like they can't respond to life events outside of their control? What could we do to support these individuals while also communicating to them that their presence is important to us - on a personal level as well as on our group project level?
Not unlike the flow chart in Spade's book, we came up with a system to prevent unnecessary escalation while still communicating how important coming to weekly planning meetings were. We created a process.
Decision-making, future plans, processes - all of these things can still happen when you do away with hierarchy and power dynamics.
You can still have people with roles that align to their strengths without elevating them above someone with different strengths.
You can still get things done.
It just requires communication and listening. I'm definitely still working on both, but being a member of anarchic spaces has challenged me to improve those qualities.
Arguably these are not just qualities of a strong community; they're also qualities of strong, genuine human connection and relationship building in your personal life.
It's disarming that capitalist societies separate personal and community skills like this, but it makes sense since those in power don't want us uniting to make a better world.
And, they feel relatively secure right now because they don't think we can turn the tides against this division.
Let's get organized and try to prove them wrong.
 Quotes were added to show which pieces were word-for-word interactions and ones I've heard repeated, not to be sarcastic or mean.