To memoize, to me, means to see some input, use some expensive and
long-running function, and then to store the output so that when the
same input is seen again, it can replace the function call with a
retrieve and copy function.
I may be missing something but can't see the difference: in tables of logs and trigonometric functions, long and expensive manual calculations were done once and the results stored so that when the same input was seen again the stored result could be used to speed up calculations.