We have always understood that parallel lines are straight lines that remain the same distance apart, and are the same length. One line may extend further out than the other line, and are no longer parallel lines.
The assumption of lines being two or more straight lines at the same distance apart from one another, is in a 2 dimensional form, because it’s a 3 dimensional world, so they assume the lines are 2 d, on a flat surface.
When one circle is inside of a larger circle, which is the same distance around it, those are concentric lines, or circular lines the same distance apart.
A circle has an entirely curved line, and another curve around it, at the same distance apart from it, are different lengths, not the same length which straight lines are when parallel.
When there are two lines of ANY shape, which is the same, and the same distance apart, they are called equidistant or matching lines, not parallel lines.
Two zigzag lines that are the same shape and length at the same distance apart, are not parallel lines, nor are they known or called parallel lines, because only straight lines are parallel, while they are all equidistant lines.
The distinction is why there are two different terms used to describe them.
If all lines of any shape, are the same shape and distance apart, we would’ve called them all equidistant lines of the same shape, no need to describe them as parallel lines, because it would mean the same thing as equidistant lines.
What is the one, most obvious difference between them, is that only two straight lines that are parallel, appear to be converging together in the distance, no other lines, so curved lines or squiggly lines aren’t considered parallel, only equidistant lines.
It doesn’t matter if they want to twist the actual meaning of equidistant, to mean parallel lines can be circles or curved lines, to support the ball Earth fable, curves and circles and zigzag lines aren’t parallel lines, only straight lines are, in daily use of the term, and in their appearing to converge together in the distance.