No, it is not wrong to call single-payer systems of socialized medicine exactly what they are, because to insist on calling them single-payer systems is nothing but semantics. In a single-payer system, each person can only have the same care. They cannot go out and get something better if they are willing to pay for it. This is simple socialism.
Single payer systems uses a collection of money from different places to pay for a certain situation. The word 'socialized' has the same meaning. I think it is a wonderful idea for people who have to maintain different types of insurance for every situation. I don't think it is wrong.