Typically in Mathematica literature references are made to Lists rather than Matrices. Matrices are just lists of lists after all.
A matrix is a special case of a list, that is, it's two-dimensional and rectangular. Matrices have a lot of special functions designed for them, and they're often treated as the mathematical object that they are than just "some arrangement of numbers". Therefore, I wouldn't say it's a good idea to define a matrix to be a list.
(On a side note, most objects are simply lists, e.g.
Plot generates a
Graphics object containing a long list of options and values.)