They can, indeed overlap in some ways and Spaces has the advantage of being far more integrated into existing workflows and apps, thus all the advantages above mentioned.
However, I think there are some differences considering the paradigm that inspires these features. Their “defaults”.
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Stage Manager defaults to App separation (every time you open an App, you create a new group).
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Spaces defaults to App unification (every App opens in the current space).
Both can make the opposite of their defaults, i.e group or separate Apps, but you must make it manually (or set a discretionary rule in the configuration).
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In Stage Manager to make apps group, one must manually drag the window from the Cast (preview) to the current Set
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In Spaces, to separate an App from its current Space, one must create a new Space (or use an existing one) and move the desired app there either via drag and drop or a keyboard shortcut (third party app may be required, I, for one, use Swish and a Karabiner Elements simlayer for that).
I’ve wrote about this a while ago here.
To sum up, it’s all about their defaults: while Spaces default to task/apps combination, Stage Manager changes the game by defaulting to task/apps separation.
I expect some of the gaps to be filled in coming months by third party software and in future macOS releases.
But even if they do: Spaces and Stage Manager were born from different philosophies on how to group/separate apps.