I don't think there is an accepted standard.

From what I gather:
'Integers' is an all encompassing term.

negative = ...,-3,-2,-1
positive = 1,2,3,....
non negative = 0,1,2,3,...
non positive = ...,-3,-2,-1,0

Whole numbers can be either 'positive' and 'non negative'.
But by this reckoning 'non positive' is equivalent to 'negative'.
very convoluted.