Line Shape

I suppose I would say only B is a line, and A, C, and D are shapes. But...

My general theory on the difference between shape and line is that shapes are defined by lines. Where as lines are defined by the space surrounding them. But this really just ends up being a fruitless attempt to define something seemingly cyclic. When I think of a shape I think of something with mass, something broad, but a polygon can take on any form. And what is a line when magnified, afterall, but a stretched and thinned polygon, a shape. Does a shape cease to be a shape when it gets thin enough that we can no longer distinguish its angles and sides? Do we then call it a line? If you scrutinize and magnify a general line until it possesses the same characteristics of a rectangle has it gone from defining a shape to becoming one, has it changed? I give up.