TL;DR:
A DTO describes the pattern of state transfer. A POCO doesn't describe anything. It's another way of saying "object" in OOP. It comes from POJO (Java), coined by Martin Fowler who literally just describes it as a fancier name for 'object' because 'object' isn't very sexy.
A DTO is an object pattern used to transfer state between layers of concern. They can have behavior (i.e. can technically be a poco) so long as that behavior doesn't mutate the state. For example, it may have a method that serializes itself.
A POCO is a plain object, but what is meant by 'plain' is that it is not special. It just means it's a CLR object with no implied pattern to it. A generic term. It isn't made to work with some other framework. So if your POCO has [JsonProperty]
or EF decorations all over it's properties, for example, then it I'd argue that it isn't a POCO.
Here some examples of different kinds of object patterns to compare:
These are all just objects, but notice that most of them are generally tied to a pattern. So you could call them "objects" or you could be more specific about its intent and call it by what it is. This is also why we have design patterns; to describe complex concepts in a few works. DTO is a pattern. Aggregate root is a pattern, View Model is a pattern (e.g. MVC & MVVM). POCO is not a pattern.
A POCO doesn't describe a pattern. It is just a different way of referring to classes/objects in OOP. Think of it as an abstract concept; they can be referring to anything. IMO, there's a one-way relationship though because once an object reaches the point where it can only serve one purpose cleanly, it is no longer a POCO. For example, once you mark up your class with decorations to make it work with some framework, it is no longer a POCO. Therefore:
The point in making a distinction between the two is about keeping patterns clear and consistent in effort to not cross concerns and lead to tight coupling. For example if you have a business object that has methods to mutate state, but is also decorated to hell with EF decorations for saving to SQL Server AND JsonProperty so that it can be sent back over an API endpoint. That object would be intolerant to change, and would likely be littered with variants of properties (e.g. UserId, UserPk, UserKey, UserGuid, where some of them are marked up to not be saved to the DB and others marked up to not be serialized to JSON at the API endpoint).
So if you were to tell me something was a DTO, then I'd probably make sure it was never used for anything other than moving state around. If you told me something was a view model, then I'd probably make sure it wasn't getting saved to a database. If you told me something was a Domain Model, then I'd probably make sure it had no dependencies on anything outside of the domain. But if you told me something was a POCO, you wouldn't really be telling me much at all.