What cache

Bit confused as to what im doing with Wp cache plugins.

When i add a cache plugin it says it will speed up page load time somehow.

My understanding of caching was that user visits my website, the website sets some caching settings somewhere which means a copy of the website will be kept on the sers device, so when they visit again most of the things are just used from this cache meaning you dont have to redownload them.

But the Wp cache plugins seem to store data on the server, then every now again you have to manually clear this cache, like when you update a post.

So is it right there are two types of caching:
User side browser cache
Server side caching.

is it better to set one or both of these. is there a plugin that allows you to set browser caching or is it set in that .htacccess file