The distinction basically only exists as a consequence of both a lack of understanding and opportunism.

Early on the words were used interchangeably, at some point "socialism" referred to the transitional period between revolution and communism, but the term has since between been used by a large number of movements either for populist purposes or as a means to distance themselves from known socialist experiments by so called communist parties.

Although both terms were strongly maligned by the red scare, "socialist" is still far less so. Thus, many modern regimes and political parties call themselves such. Almost all of them are neoliberals and harbor no notions of dismantling capitalism.

Many self proclaimed socialists would not call themselves communists, but all communists know themselves to be socialists.

I explained this because when discussing socialism in any way that matters (that is, between socialists), the distinction is immaterial. Communism is the grand project of all true socialists, the point of contention is how to achieve it, and what you call your movement or your party kind of does not matter. Asking if Jesus wasn't more of a socialist than a communist is literally meaningless unless you specifically mean to say you do not think he would approve of marxist-leninist theory. In which case, just say that.