What is the difference between intrinsic and extrinsic apoptosis?
In both pathways 'the cell does itself' the difference is in the reason.

In short:
Intrinsic apoptosis is a response to 'internal damage' eg. damaged DNA, chromosom rearrangement, hang ups in division, hypoxia, etc. that the cell senses itself and 'decides to commit suicide'. This is done by the mitochondrial pathway - release of cytochrome C from the mitochondria activates the caspase cascade that results in programmed cell death. This is like "I'm too damaged, I must die".

In the extrinsic pathway as you have mentioned is indeed related to the FAS ligand (and Fas/FasL being the main pathway for apoptosis), but that is not the only external signal as TNF (also known as TNA-alpha) binding to TNF-R1 (tumor necrosis factor receptor 1) may also lead to apoptosis. These pathways are usually activated by the immune system for example in cellular immune response. This is like "You're abnormal / dangerous / infected, you must die".

Both pathways activates the caspase cascade at some point that results in apoptosis. Either way the actual process of apoptosis is carried out by the cell itself in a programmed, regulated manner.

Source: http://en.wikipedia.org/wiki/Apoptosis
This papaer offers a great review on the topic, including both pathways:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2117903/

I'd like to quote few  important parts to support my answer:


  The extrinsic, intrinsic, and granzyme B pathways converge on the same terminal, or execution pathway. This pathway is initiated by the cleavage of caspase-3 and results in DNA fragmentation, degradation of cytoskeletal and nuclear proteins, cross-linking of proteins, formation of apoptotic bodies, expression of ligands for phagocytic cell receptors and finally uptake by phagocytic cells. 


(...)


  The extrinsic signaling pathways that initiate apoptosis involve transmembrane receptor-mediated interactions. These involve death receptors that are members of the tumor necrosis factor (TNF) receptor gene superfamily


(...)


  The intrinsic signaling pathways that initiate apoptosis involve a diverse array of non-receptor-mediated stimuli that produce intracellular signals that act directly on targets within the cell and are mitochondrial-initiated events.