Hi soul, I am not sure if I know what you're trying to do.
Do you want same shapes to match the size and outline of each other? Or do you just want them to snap?
You would use snap to layers for that. If you are trying to transform them, match the centers, hold down alt/opt + shift and move a handle. This will transform from the center.
If you have let's say, a square of texture or design and you want it to fit the exact shape of image 1, you want to create a clipping mask. This will confine the above layer of image 2 to the outlines of image 1. You will only see image 2 coming through image 1. You can then move the #2 layer around or transform it's size, shape, etc., using normal transform commands.
To clip one layer to the layer below, I like to hold down alt/opt and click the cursor at the line between the two layers. It's also under layers, but I like the keyboards short cut.
Let me know if I'm way off the mark or not!