Since the 8938 actually accompanies your federal income tax return, your filing status determines the reporting thresholds as well as the way you report the assets (just yours for single and married filing separately, and all combined for a joint return). So yes, you would definitely have to file separate tax returns (often not a good idea) if you wanted to file separate 8938s.
Assuming you do file jointly, there is indeed no distinction made between the assets owned by the two spouses (as you can see on the actual form). There are a couple of “account jointly owned with spouse” checkboxes, but otherwise they’ve decided this is something they don’t need info about. Thanks @liuxuhan2021!
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