Set, list, array, these are all words to describe collections of numbers, including an NxM array. But a matrix it's a very specific thing, it is not just an arr

Set, list, array, these are all words to describe collections of numbers, including an NxM array. But a matrix it's a very specific thing, it is not just an array of numbers, it is a mathematical object with defined mathematical functions applicable to it, as such it does define a set of linear combinations. Similarly, there is a difference between an N-element set of numbers and an Nth dimensional vector.