Consider $P(x_1,y_1)$, $Q(x_2,y_1)$, and $R(x_2,y_2)$. In this case, the distance between $P$ and $Q$ is $|x_2-x_1|$ but the signed distance from $P$ to $Q$ is $x_2-x_1$. Similarly, disntace between $Q$ and $R$ is $|y_2-y_1|$ and the signed distance from $Q$ to $R$ is $y_2-y_1$.
Regular distance is usually denoted by $|PQ|$ or $d(P,Q)$. So $$|PQ|=|x_2-x_1|,\quad |QR|=|y_2-y_1|.$$
I am not sure about the signed distance. I've seen in some old textbooks that they are denoted by $PQ$ and $QR$ and even sometimes $\overline{PQ}$ and $\overline{QR}$ (especially in some French and Russian books). But over line is now reserved for line segment.
How is signed distance denoted nowadays? Is there anther terminology used for signed distance?
It is typically denoted by or , as you mentioned. It is also sometimes referred to as directed distance or oriented distance.
In general, the notation for signed distance can vary depending on the context and the specific conventions being used. It is important to carefully review any documentation or instructions provided to ensure that you are using the correct notation for the task at hand.