Browser cache
The visitor's own copy, controlled by response headers. Excellent for versioned assets, dangerous for HTML — a long cache lifetime on a page means visitors see yesterday's content with no way for you to clear it.
Server and object cache
Full-page caching stores rendered HTML; object caching stores the expensive intermediate results, usually database queries. Object caching helps logged-in traffic that cannot use a page cache.
CDN
Copies of your assets nearer the visitor. The most common misconfiguration is caching a page containing personalised content, which then gets served to everyone.
