VPS plans are similar to shared plans in that both feature multiple websites hosted on a single server. However, VPS plans maintain a strict separation between clients and websites when it comes to resource allocations. Your site gets its share, and no one else may use your resources (conversely, you may not cannibalize the resources allocated to others' websites either).
Moving to another website consists of transferring the website’s files and databases, configuring your site with the new host, and directing your domain’s DNS to the new host. Once you pick a new site host, they can usually help you out with this process. The cost will depend on the host you’re switching to, but it will probably be anywhere from $150-$400.