You are “right” in a purely colloquial sense, since statements like yours are precisely the reason socialism now means about a thousand different things to a thousand different people.
But actual socialism, not the casual use wherein it’s a substitute for the word “welfare”, is when wealth is owned & regulated in a collective sense. It is community exchange, and community ownership.
Welfare is only arbitrarily similar to how a socialist economy operates. But there is no actual communal or worker owned means of of production. It is just a social band-aid funded through high taxes within a Capitalist system of privately owned capital.