Technically (the best kind of correct), it's not "THE PARTY", it's the Community that administers the means of production.
This could be, as you say a political party, electronic plebiscite, a nominated/elected committee, WORKERS, or even Anarcho Socialism.
There are also different flavours of "Owning the means of production".
You could have the USA style of Socialism, where Space Craft Development, Military Development, Road system is owned by the taxpayer (😁) or a more mainstream Socialism where say Industry is Socially owned and Small retailers and Trades are private.
The major problem with Perception of Socialism in the USA specifically (and it's vassal states like Australia), is that the Communists perception of Socialism is used. A transient state before full Communism.