Since 90=90, they are technically in the same place. For a symmetrical earth.
BUT - if the earth isn't symmetrical, so that at the geodetic north pole - where the horizon is at right angles to the pole on the equator - you could drill "straight down" i.e. at right angles to the local horizon and NOT hit the centre of the earth, then they wouldn't be the same place.
I can't see how that's a practical possibility for the earth, but maybe some smart geographer has found the earth's a bit squint.