Game server question

My friends and I were thinking about renting a server for Counter-Strike: Source. We have never done this before, and we came across something that confused us(smart as we are ). What is the difference between a public server and private server? The private ones are cheaper.

 

All you need to host a server is a computer and an internet connection.

A public server : anyone can join; A private server : anyone WITH THE PASSWORD can join. i.e. its password protected. Generally, they arn't listed on public server lists (i.e. when you go "Internet Game" it won't show your game up), so you need to provide an IP/domain complete with port number.

Typically, private servers are used for clan matches etc.

The reason they are cheaper is because generally they require less maintainance (the public means people who hack/cheat whatever, therefore you need an admin to kick those people. If its a private server, usually one person gets given the privs to kick somone if they are suspected to be cheating)