I looked up that James Whitaker (the one with the Chelsea Pension) and he went to Sierra Leone.
Where did you find that he went to Sierra Leone?
I think it is very likely that the pensioner who died in Bury in 1844 was the same soldier who deserted on Christmas Day 1801.
There are possible explanations for the discharge date disparity:
1. a short period of further service between approval of discharge and actual discharge (very common), or
2. a delay between discharge and being accepted for out-pension, for some reason.