160 is a little high, but if this is the first of second time for her in the stairclimber then it’s normal (you will need to monitor for any distress signs). HR on the bike will always be lower than the stairclimber for obvious reasons. Each person reacts differently to various intensity levels and what seems difficult for one person it might not be for another. If she is in good health condition and she feels comfortable at 160 bpm despite her age I wouldn’t worry too much. RPE scale is a great way of finding out how she really feels. The same goes for any of the other machines.