vpn != vps, vpn is a tunnel so you access the internet through some proxy (usually some institution like a college campus, so you can access paid services that they provide to students free). vps is some server you purchase, not necessarily linked to your identity or your ip address (if you pay with a visa gift card, for example), usually in some datacenter somewhere alongside thousands of other servers.
vps is more difficult to track you - police have to issue a warrant to the server host to get your ip address and maybe your isp (which is complicated by the fact that all the traffic from the server comes from the same or similar ip's and may not necessarily be linkable back to a single account), then issue a warrant to various ips for your personal info. generally not worth unless you're some big seeder or something. most vpns on the other hand can and do associate all your traffic with your ip address, and so are able to turn over that info on demand much more easily.