Does this kind of logical fallacy have a name?
Apples are fruit. Oranges are fruit. Therefore, apples are oranges.
I'm guessing it's a particular kind of statistical syllogism?
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It is the Fallacy of the undistributed middle:
All Apples are Fruit
All Oranges are Fruit
Therefore, all Apples are Oranges
is clearly invalid.
I believe that is the fallacy of undistributed middle. The middle or shared term or class, "fruit", remains undistributed in either premise. For a more complete discussion of this fallacy, you could take a look at this brief introduction.