We can represent a line in 2 and 3 dimensions using 2 and 4 parameters respectively.
For example, in 2 dimensions, we can represent a line using the angle $\theta$ of the normal and orthogonal offset $t$ of the line from the origin. Or, we can use points $x,y$ where $\theta = \text{atan2}(x,y)$ and $t = ||(x,y)||$.
This is in contrast to typical line coordinates, which I believe use three parameters.
I am wondering if there is a vocabulary to describe these different representations of lines.