Please see the Description sections on the documentation pages for the isscalar, isvector, and ismatrix functions for a definition of what MATLAB considers a scalar, vector, and matrix to be. You can find all three of those functions linked from this documentation page.
Everything in MATLAB can be considered an array, but usually when I use the word array instead of matrix I'm using it to denote either something with an unknown or unspecified number of dimensions (possibly greater than 2) or to denote something that I know has more than 2 dimensions.
"The sin function accepts an array x and returns an array y of the same size. Each element in y is the sine of the corresponding element of x." Here, I don't know how many dimensions x has so I use the most general term. The statement is true whether I call sin on a scalar, a vector, a matrix, or a 1-by-2-by-3-by-4-by-5-by-6 array.
"A truecolor array has three pages: one for the red component, one for green, and one for blue." Here I know that the thing to which I'm referring, the truecolor image, has three dimensions so it's not a matrix. "Calling the magic function as magic(n) returns the n-by-n magic square matrix." By definition magic returns a 2-dimensional array so using the word matrix is accurate and most specific.
And yes, I know magic(2) doesn't return a magic square.
