Difference between $SO_n(\mathbb{R})$ and $SU_n(\mathbb{R})$.

Question

Is there any difference between the real Lie groups $SO_n(\mathbb{R})$ and $SU_n(\mathbb{R})$ or similarly the Lie groups $O_n(\mathbb{R})$ and $U_n(\mathbb{R})$. It seems that usually when talking about Lie groups we mean real ones but it seems like these groups should be the same in this case.