Collarable and tame open manifolds

Question

Let $M$ be an open manifold (which means non compact and without boundary), and let us assume that $M$ is $1$-ended, i.e. it has only one topological end. $M$ is said to be collarable if there exists a collar neighborhood of infinity, i.e. a neighborhood of infinity which is of the form $N \simeq \partial N \times [0, + \infty)$. There is a famous theorem due to Siebenmann which gives necessary and sufficient conditions in order for an open manifold to be collarable. Now, it seems to me that this condition is equivalent to the fact that the manifold is tame, i.e. it is homeomorphic to $M' - \partial M'$, where $M'$ is a compact manifold with boundary. In fact, our $M'$ is given by the union of the "compactification" of the collar neighborhood and its complementary. Am I missing something? For more precise definitions I leave here the following link https://arxiv.org/pdf/1210.6741.pdf .