Self-managing teams (Scrum Guide 2020) vs Self-organizing teams (12 Agile Principles)

I would say that Self-Organizing is only one aspect of Self-Managing.  Self-Managing is much more than just how they organize. Also note that the Agile Principles have not been updated in more than 20 years while the Scrum Guide evolves as how people work does.

I understand the phrase "self-organizing team" to mean that the team chooses how to go about doing the work and the phrase "self-managing team" to mean that the team also chooses what work to do and when to do it. A self-managing team must also be self-organizing, but a self-organizing team doesn't have to be self-managing.

The Manifesto for Agile Software Development sets down a foundational principle that teams are self-organizing. A team that is unable to choose how to do the work is unable, or at the very least, hampered, in their ability to be agile and responsive to the changing environment. The Manifesto doesn't necessarily require that teams be self-managing. A team that is told what work to do or when to do work may still be agile, at least the way that Agile Software Development was defined in the early 2000s.

Scrum takes it a step further, however, and requires self-managing teams. Partly, this is enabled by putting the Product Owner on the Scrum Team. By putting the Product Owner on the Scrum Team and making the Product Owner accountable for the ordering of the Product Backlog, the Scrum Team has the ability to decide what work to do (or not do, by not putting it on the Product Backlog) and roughly when it will be done (by setting Product Goals and Sprint Goals and ordering the Product Backlog to support those goals). If the Scrum Team is not able to do these things and be self-managing, you do not have a Scrum Team and are not practicing Scrum.

A previous discussion here on the Scrum.org forums may also be relevant.

The most effective way to inspect and adapt is as closely as possible to the time and place of work being carried out. We should aim to have self-managing, self-organizing, self-directing, self-orchestrating, self-steering, and self-monitoring teams.

All these are good, but to varying degrees, each of the above concepts is also disruptive and potentially challenging. For example, "self-managing team" could trigger a reactionary manager into thinking he or she is being sidelined, whereas "self-organizing team" might not. So think about how such terms will land when you use them. Choose your language according to the maturity of your audience and try to meet them where they are. There are hills worth dying on, but it can sometimes be best just to choose the words which are least likely to get you fired.

Thanks all for your valuable insights. These really helped.