Why we treat sentence letter $Q$ as conclusion in one form and premise in other?

Question

Sorry for asking such a dumb question.

I am CS student and I am trying to understand the basic tenets of Logic. I am new to the subject and I am lost understanding Implication.

In formal logic, $(P\rightarrow Q)$, The sentence letter $P$ is premise and $Q$ is conclusion, right?

Now, we know that $(P\rightarrow Q)$ is equivalent to $-(P\wedge -Q)$ i.e. It is not the case that $P$ and not $Q$. Here, $Q$ acts as premise, right?

So, why we treat sentence letter $Q$ as conclusion in form and premise in other?