Hi

Shared hosting:

A shared hosting is cheapest hosting type. There you share system resources with lots of neighbors, free system resources automatically helps busy websites but in return your website can go down because of load on other websites on your server.

VPS hosting:

VPS hosting is also shared but allocated system resources are provided to every website separately, no one uses system resources of others including bandwidth. Webmasters can install their own softwares and tools because they get more control on server.

Hope this helps you.