They are both equivalent. Throughout my education (I did a maths degree as well), the terminology was almost always 'commutative LAW of addition'. Keep in mind 'Law' and 'Property' are synonyms in this context.

Thanks for the answers.

Here's how I would write it. Depends whether you are writing for maths graduates, maths majors or the general public. A property is an attribute of a thing. A property of my car is that it is a silver-grey colour. So, a concept, such as a group or a ring or the set of integers with the operation addition may have a property such as being commutative. The integers have the property of being commutative under addition. A law describes a possible structure possibly including how it is written or how it works. Such as being commutative. The law of something A being commutative under an operation "+" means that for a & b from A; a+b = b+a. Obeying this law is a property of the integers under addition. . I suspect Thomas has a small typo when he writes "communitive".

Communitive property of addition is the correct term. Some people say communitive law but this is incorrect.