Of course insurers transfer money. Spreading risk involves transferring money. If you and I both pay premiums to Geico and you get in an accident but I don’t, my premiums help cover Geico’s payout to you.
The key word is IF. Insurance only pays when there is an incident. So it doesn’t transfer your money your money to someone else. Your money is invested by the insurance company. It goes nowhere unless there is a claim which is paid from the investment pool.
Social Securtiy is welfare. It takes from today’s worker and gives to today’s recipient. There is no risk coverage since everyone gets it. It is not insurance.