European countries used food stamps during WW2. It implies that country does not have enough food, if it has to ration its food supplies. I know it is social assistance, but it has really bad name.

NHS is paid health insurance, sometimes pretty expensive, not much relevant.

US 'food stamps' (for which the actual name is the Supplemental Nutrition Assistance Program) are actually just a government-issued debit card that can only be spent on food at most private retailers. There's absolutely no connotation of rationing in the US nor is there any stamp involved.

You are confusing rationing with (essentially) gifting.

Ration stamps merely represented a limited ability to buy a resource in short supply. For example, if you had ration stamps for gasoline/petrol, you could buy up to whatever quantity you had stamps for -- you handed over the stamps and cash.

The term "stamp" in this context is used to refer to a system of payment using a proof-of-purchase (the stamp). Another example, a postage stamp is evidence that you have paid for the delivery of your letter. Some countries use stamps to pay for government services like deeds or passports.

You are confusing this with a ration system using stamps, which allows the purchase of a good, but does not actually pay for the goods.

You should probably look up what food stamps are in the US. They have nothing to do with a food shortage.