A number can either have non-zero values after the decimal point (a fraction) or only zeros (whole). An integer must be whole; it can be negative(-55,-1,etc.), positive(7000,2,etc.), or zero.
"Number" is a general term. Integers are a specific kind of number: positive whole numbers, negative whole numbers, and zero. A "whole number" does not have any fractional part - so 6 is a whole number but 6.25 is not. Numbers with decimals are not integers - but they're numbers.