HI Eden,
You can think of a Curve (in its simples form, without any Extrusion or Bevel) as a bent line segment and there is a 1 to 1 mapping between that line segment and the U-‘axis’ of the (2 dimensional) UV ‘space’. The U and V both go from 0 to 1 and the beginning of the Curve is being mapped to point (0, 0.5) of the UV ‘space’ and the end to (1, 0.5) and one-eigth of the length of the Curve is mapped to (0.125, 0.5), etc.
So basically, a Curve becomes un-bent in the UV ‘space’. A Curve Circle is being mapped to a straight line.
Meshes are discreet and each Vertex (or actually each Face Corner) is being mapped to a point in the UV space and then everything between those points is being interpolated, so a Mesh with more Vertices will give a better (more accurate) UV Mapping.
Curves are mathematical objects, but in Computer Graphics, not all points of a Curve are being calculated; the Resolution (default is 12), tells Blender how many points of the Curve, between each Control Point (which is sort of like a Vertex for Curves) are being calculated.
