> The name "ones' complement" (note this is possessive of the plural "ones", not of a singular "one") refers to the fact that such an inverted value, if added to the original, would always produce an 'all ones' number
The radix complement in base two. They are closely related but not identical - the two's complement representation of a negative number is the ones' complement representation + 1 (ignoring the final carry). In ones' complment there are two representations for 0 (all 0s or all 1s), but every number has a positive and negative representation. In two's complement, there is a single 0, but there is also negative number that doesn't have a corresponding positive representation (INT_MIN).
In fact, for every numerical base there is an equivalent. For example, in base 3 you can represent a number in twos' complement notation (each trit X is replaced with 2-X, so -3 is represented as 212 on three trits, with +3 being 010) is or in three's complement by adding 1 (212+1 = 220). For base 10, you can do nines' complement (-3 on 3 digits is 996) or ten's complement (996+1 = 997).