A line is a series of points that are strung together.
Based on this free form definition, the line theoretically can have infinite combinations.
You can have a curve line, an s-curve line, a multiple curve line, a periodically curved line like a Sine curve, you can have an exponential line, a logarithmic line, a parabolic line, hyperbolic line, elliptical line and circle line, .. etc.
You can even have a messy line, something a child loves to do. Combing with the above, you can have a bold line, a thin line, a variable thickness line, etc.
Throw in colors, you have a yellow line, red line, blue line, green line, purple line and even rainbow-colored line, etc.
Add in a multiple, you can have double line, triple line, broken line, and more.
With all these combinations, there should be infinite number of line types.
Add in the third dimension, you can have a helix line, double helix lines, etc, etc.
Add in the nth dimension ... will let you figure this out.
If between two points, the line has the shortest distance, then it is also a straight line.