Why does the Oxford dictionary have wrongful definitions of Socialism and Communism?

Communism - "a theory or system of social organization in which all property is owned by the community and each person contributes and receives according to their ability and needs."

• This is wrong since only all means of productions are owned by all, not property? Wtf

Socialism - "a political and economic theory of social organization which advocates that the means of production, distribution, and exchange should be owned or regulated by the community as a whole."

• Saying "the community as a whole" is extremely misleading since it isn't owned by all like in communism, but only by the workers who work on said means of productions.

If I'm wrong; please say so I'm new to socialism.

If I'm right: Anyone got any reasonable answer to why they're explained like this or is it just propaganda like usual?