ATF is a hydraulic fluid, so there really is no discrepancy.
Did the manual specify a particular spec (viscosity) of hydraulic fluid, e.g. AW 32 or ISO 46? If so, that's the best choice, but not the only acceptable one. If it just says "hydraulic fluid", then ATF qualifies as one of the several available types. And ATF is compatible with the jack hydraulic system (brake fluid is not).
Personally, I would just go ahead and use the ATF, since it is clearly labeled for it.
2004 American Tradition; 2014 Buick LaCRosse
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