Tangent space of a submanifold vs tangent space of an open set in a manifold

Question

Let $M$ be a smooth manifold. I learned that if $U$ is an open set in $M$ then the tangent spaces of $U$ are equal to the tangent spaces of $M$ at every point. On the other hand, if $N$ is a submanifold of $M$ then a tangent space of $M$ may not be the same as a tangent space of $N$. I'm confused in why this is true even though a submanifold of $M$ is an open set in it. (I apologize if my question is very stupid ).