It's welfare, and completely different to a "any pension scheme" - you neither save nor have a a defined benefit. All your NI payments do is gain you an entitlement to some form of state pension at a variable date in the future, and go in the pot as per any tax.
None of us started paying NI with a contract to get a guaranteed amount, at a guaranteed date, with a guaranteed annual increase. It's bizarre that people talk as if that's what they've done.