Question about Function Transformations?

So I am learning about transformations applied to a function for y = f(x) and I was a bit unsure about dilations. If the graph was to shrink or stretch in the y direction (i.e. y = af(x) ), would that mean it is a dilation FROM the x axis? Would these different ways of saying it mean the same thing? Similarly, If a graph was to shrink or stretch in the x direction (i.e. y = f(ax) ), would it be correct to call it a dilation from the y axis?