VPN doesn't give you privacy; it only allows you to bypass blocks (and introduce yourself to blocks in other countries or services though). VPN providers can still log your every move.
The difference is, VPN providers, unlike ISPs normally don't have your home address and passport info[1]. Some don't have your name at all, unless your traffic leaks your identity - e.g. when you're paying for VPN service with Bitcoin. Even more, they're generally out of your jurisdiction, which acts as some barrier against frivolous requests.
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[1] In Russia every ISP is legally required to perform this sort of KYC and keep those records for a while.
