qualitative vs quantitative difference

[Hrvoje1]

That difference between these two differences can be defined like this:
Consider two objects o1 and o2, if they share common property p, for which subtraction is well defined operation, then the quantitative difference between them with respect to property p is o1.p-o2.p, where the operands are values of property p of objects o1 and o2 respectively. If the property p is not common, that is, not defined for any of the two objects, then this condition can be defined as qualitative difference between them, another definition that can be introduced is that we can say that they are not instances of the same class. From that definition follows that in order to belong to the same class, objects must have in common all their properties. From there naturaly arises the extension operation with respect to uncommon properties, that can be defined on classes, which removes the qualitative difference present with respect to uncommon property, by assigning the value zero to the property in a class in which the property is originally missing. For example, 2D point class of objects, can be extended to 3D class of objects, by assigning zero to the third coordinate that is originally missing in 2D point class. 
Let us define that classes can consist additionally of methods, besides properties, and that methods can be implemented, in which case classes are called concrete, and they allow instantiation of objects, otherwise they are abstract. In that case, abstract classes may be defined as qualitatively same, if they have same properties and methods, and criterion of equality of methods is that they have same names and signatures, that is input and output argument names and types. Concrete classes methods must have the same implementation additionally, in order to be qualitatively equal. I do not see sensible way of defining quantitative difference on objects of the same class, with respect to methods.
What did I just describe? Is it already covered in some mathematical discipline, or is it just a philosophy based on object oriented programming paradigm?