The order is the highest derivative in the equation and the degree is the power of this derivative after the equation has been put into rational form and cleared of fractions. So the answer is -no- you are not correct. The orders are indeed 2 but the degree is in both cases ...
Let's give a more complicated example:
Here we have order 2 (highes derivative is y") and degree 2 (the power is 2, don't forget to eliminate the common y").
Do you see what your degrees are now?