Yes, I am not sure I understand the question. First, as you said, the sine is a ratio, not a side, unless the hypotenuse has length 1. Second, it's the ratio of the opposite side (and not the adjacent side) to the hypotenuse by definition.

Are you asking why every right triangle with the same acute angle has the same ratio of the opposite side to the hypotenuse? This is because all such triangles are similar.