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...
fastcgi_cache, we cache output from PHP directly.
There are few more types. For example,
uwsgi_cache mostly used by Python apps.
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).