I found two different looking things being called the Littlewood-Offord theorem,
If $\vec{a} \in \mathbb{R}^k \setminus 0$ and $t \in \mathbb{R}$ then there are $O(\frac{2^k}{\sqrt{k}})$ points $x \in \{1,-1\}^k$ such that $\vec{a}.\vec{x}=t$
If $\vec{a} \in \mathbb{R}^k$ is such that at least $n$ of the $a_i$ have $\vert a_i \vert \geq 1$ then for $x \sim \{1,-1\}^k$ uniformly at random and $I$ an interval of length $2$ we have $Pr_x[ \vec{a}.\vec{x} \in I] \leq O(\frac{1}{\sqrt{n}})$
Can someone kindly explain if these two are related to each other or not? Is one derivable from the other?
Can someone give an expository (lecture notes) reference of the proof of the later version?