It is referred to as:
a fog line,
a lane marker,
an outside lane marker,
a right lane marker,
a lane delineator or
the edge of the roadway.
They are all pretty much interchangeable terms. The line defines the border between the roadway and the shoulder. If you drive to the right of the line, you are off the roadway, on the shoulder, but still on the road.
In most cases, the line is merely a guide that that used to determine if you are on the roadway or not. Case law states it is a "guideline for safe driving and may be crossed minimally, as needed for safe operation except in cases where it is prohibited by law* or would endanger others."
*21755 CVC states The driver of a motor vehicle may overtake and pass another vehicle upon the right only under conditions permitting such movement in safety. In no event shall such movement be made by driving off the paved or main-traveled portion of the roadway.
This is one section that can be used in a lane sharing defense. But it is a double edged sword; If you cross over the fog line, you have driven off the roadway and are in foul territory for a 21755 violation.
The case law refers to the white lines and crosshatched areas at the freeway on/off ramps and people crossing them to merge early or get off late. That is something that may be done, if done safely and without interfering with other vehicles.
I was skipping clover leaves and maybe thought it was one or something. 
