All tutorials here - http://rtcamp.com/wordpress-nginx/tutorials
Above link has a matrix of all config for easy access.
SIngle-site configs - http://rtcamp.com/wordpress-nginx/tutorials/single-site/
Multisite configs - http://rtcamp.com/wordpress-nginx/tutorials/multisite/
Even I am not happy with new layout. This is better than blog posts but may not scale well few months down the lane!
I am thinking of moving all tutorials to a MediaWiki or some other kind of wiki setup!
Anyway... Coming back to your question...
proxy_cache
is used in most WordPress-Nginx tutorial to cache output of Apache in Nginx. In those cases, Apache handles PHP which is not only slower than our way but a stupid way to config Nginx! Why get Apache involved when Nginx can talk to PHP directly...
In fastcgi_cache
, we cache output from PHP directly.
There are few more types. For example, uwsgi_cache
mostly used by Python apps.
We use proxy_cache
when using Nginx as load-balancer. In those cases, Nginx talks to few more Nginx behind the scene (on another physical server most likely).