Instead of describing what these two classes do, it would be better to describe what it actually means for something to be read-only or immutable, as there is a key distinction which doesn't really give much option to those two implementations.
Read-only is part of an "interface" of a class, its set of public methods and properties. Being read-only means that there is no possible sequence of actions an external consumer of the class could do in order to affect its visible state. Compare with a read-only file for example; no application can write to such a file using the same API that made it possible to make it read-only in the first place.
Does read-only imply thread-safe? Not necessarily – a read-only class could still employ things like caching or optimization of its internal data structures and those may be (poorly) implemented in a way that breaks when invoked concurrently.
Does read-only imply never-changing? Also no; look at the system clock, for example. You cannot really affect it (with the default permissions), you can only read it (making it read-only by definition), but its value changes based on the time.
Never-changing means immutable. It is a much stronger concept, and, like thread-safety, is a part of the contract of the whole class. The class must actively ensure that no part of its instance ever changes during its lifetime, with respect to what can be observed externally.
Strings are immutable in .NET: as long as the integrity of the runtime is not compromised (by memory hacking), a particular instance of a string will never be different from its initially observed value. Read-only files are, on the other hand, not much immutable, as one could always turn read-only off and change the file.
Immutable also does not imply thread-safe, as such an object could still employ techniques that modify its internal state and are not thread-safe (but it's generally easier to ensure).
The question whether immutable implies read-only depends on how you look at it. You can usually "mutate" an immutable object in a way that doesn't affect external code that may be using it, thus exposing an immutable object is at least as strong as exposing a read-only one. Taking a substring of a string is like deleting a part of it, but in a safe manner.
This brings us back to the original question about the two classes. All ReadOnlyDictionary has to do is to be read-only. You still have to provide the data in some way, with an internally wrapped dictionary, and you and only you can still write to it through the internal dictionary. The wrapper provides "strong" read-only access (compared to a "weak" read-only access that you get just by casting to IReadOnlyDictionary). It is also thread-safe, but only when the underlying dictionary is thread-safe as well.
ImmutableDictionary can do much more with the strong guarantee that the data it holds cannot be changed. Essentially you can "patch" parts of it with new data and obtain a modified "copy" of the structure but without actually copying the complete object. It is also thread-safe by the virtue of its implementation. Similarly to a StringBuilder, you use a builder to make changes to an instance and then bake them to make the final instance of an immutable dictionary.