Difference between tangent spaces of O(n, R) and SO(n, R)

Question

I know that $O(n, \mathbb{R})$ is a group of nxn matrices satisfying $X^TX=I$, and $SO(n, \mathbb{R})$ has additional condition of positive determinant. But I have no idea about how could those groups' tangent spaces be different. What's the difference?