In a normal corporation, the investors delegate control to a board of directors and the board decides whether to retain profits or pay dividends and hire/fire the CEO.
In DAC/DAO/DO, the investors actively vote on issues. The distinctions between those three have to do with the structure of this control...
Let's first review Vitalik's chart below:
Note Vitalik's conceptualization is actually not wrong, but too abstract and what The DAO codified is what I think is incorrect. I like Vitalik's chart except DAOs have humans in control ("in the center") but they are governed by protocol (which is probably what Vitalik means by "automation"):
Notice on "Internal Capital" table, the horizontal line separating "Automation at the center" at the top from "Humans at the center" at the bottom is labeled "DO" for decentralized organization, because "DO" is decentralizing the "Humans at the center" but not automating the decisions of protocol at the center controlling the "Human at the edges" (where edges means who do the work).
And the vertical line separating "Automation at the edges" on the left from "Humans at the edges" on the right is labled "Tools" because they are doing the majority of the work but not automating (thus still requiring human workers for) their operation.
You can see that table is quite insightful and abstract. This is an example of why people think of Vitalik as genius. But it is all quite obvious if one were to sit down and think about deeply for a while as obviously Vitalik did.
Now I am going to demonstrate (in a very sleepless and almost delirious mental state so please excuse the low quality of the prose) I am an abstract forward/deep/paradigm-shift thinker similar (but different of course) to what some people observe/praise about Vitalik.
It is on the term "autonomous" that Vitalik's taxonomy gets murky (muddled) as he admits. It appears that Vitalik conflated "automation" with "autonomy". It appears that Vitalik thinks that we require automation in order to obtain autonomy.
Here is the insight that occurred to me in the past 48 hours or so (the days have all run together). Whereas, I am thinking the autonomy attribute is applicable to the "humans in the center" involved in the control. In other words, DVCS open source enables each human participant to be autonomous because each can have their own individualized repository. Automation has nothing to do with it. The key technological breakthrough for DVCS was the relative changeset logic, using a hash to identify changesets, and storing the repositories locally, which isn't automation but rather a protocol for destructuring to increase degrees-of-freedom, i.e. removing hierarchies.
So whereas for Vitalik the distinction between a "DAO" and a "DO" is the former has complete A.I. automation over all decisions controlling the humans at the edges, i.e. like a master 1984 enslavement computer, I rather conceive that the "DAO" as destructuring (perhaps even automated) protocol which enables humans at the center to be autonomous. And the "DO" is many decentralized humans in the center, but they are bound together with less degrees-of-freedom in the structure enforced by the protocol that governs (i.e. by-laws for) their organization.
For example, my understanding of DASH's protocol for stakeholders is limited, but I assume it is based on a majority vote and there is no way to opt-out other than to sell your stake (unstake your masternode deposit), and thus the humans in the center controlling it are not really autonomous, thus DASH is a "DO" not a "DAO". And The DAO wasn't autonomous either and that was its critical flaw (other than the bug that enabled theft of funds) in that individual humans could not autonomously elect projects (and splitting had flawed game theory), so it couldn't be anything more than a power vacuum (slush fund) with spoils to whomever could win in the voting game theory. The DAO was worse than if the participants had invested in individual projects separately, thus the only purpose of the DAO was a game theory around controlling the pooled funds. No individual autonomy for the investors. The Ethereum and DAO developers appears to be so strongly into automation (and creating a master 1984 enslavement system? or is this just their Millennials Warcraft game A.I. culture?), that they built a DAO which was less autonomous than if each investor invested in projects separately from the DAO.
A Dash consultant Ira Miller wrote something similar but with different conclusions to mine:
https://medium.com/@gitguild/not-too-late-for-humans-to-save-ethereum-2f42f5fdfb75
Vitalik goes on to compare DAO to Dan Larimer's DAC, with the key difference being that profits are not retained in the latter. Retaining profits in the collective pool lowers autonomy, so actually DAO = DAC except when it is a non-profit. Vitalik seemed to think retaining profit (i.e. the organization is profitable) is non-profit if the profits aren't distributed back to the humans at the center. Whereas, I think the distinction is that retained profits indicates a "DO" because the stakeholders are no longer empowered to take their capital away except by selling the token which is not the same because liquidity of the float is not the same as distributing profit, i.e. 20% of the stakeholders can't sell their tokens at once to protest a vote of the majority. The DAO offered a split feature but the game theory was flawed.
I have more to write when I am not so delirious from lack of sleep. This is just a first draft to get some of my ideas written down. I'll need to expound on the differences between Ira Miller's perspective and mine.