Difference between Relative path and absolute path in javascript

Question

Have small clarifications,

As of my knowledge, these are the relative and absolute paths,

Completely relative: <img src="kitten.png"/>   
Absolute in all respects: <img src="http://www.foo.com/images/kitten.png">

What distinguishes a relative path from an absolute path?

If you use these pathways, do any performance difficulties occur?

Will the sites be safe in any way? Is it possible to change an absolute route to a relative one?