They differ at the one stereocenter - axial and equatorial only apply to one of the two possible chair forms.
Technically glucose is (2R,3S,4R,5R)-2,3,4,5,6-Pentahydroxyhexanal while mannose is (2S,3S,4R,5R)-2,3,4,5,6-Pentahydroxyhexanal The difference is at C2 - note that glucose is R and mannose is S. This doesn't change when the cyclic hemiacetal is formed.