How to prove $n$-to-$1$ mapping property for Blaschke products?

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I have two questions regarding the Blaschke products.

1) I came across the following post

Boundary behaviour of finite Blaschke products on the unit circle

where it's mentioned that for any $\lambda\in \mathbb T$ (unit circle), the equation $$B(z):=\displaystyle\prod_{k=1}^n\dfrac{z-a_k}{1-\overline{a_k}z}=\lambda$$ has $n$ distinct solutions. In this equation, $a_k\in \mathbb D$ (open unit disk). How to prove this? If it's a standard result, then a reference would be welcome!

2) In an attempt to find similar questions, I came across the following

Is a Blaschke product/rational function a covering map for a $n$-sheeted covering of $S^{1}$?

which I think is saying the same thing in my question above. If it is saying the same thing, what would be a good reference to understand the argument presented?