I am not sure what this debate over the proper definition of socialism is all about. You are simply discussing two connotations of the same word.
In the end, any difference in meaning is irrelevant because both connotations describe a political philosophy that results in more state control, an ever-encroaching police state, and an unsustainable economic model that ultimately fails and causes much pain and suffering.
A connotation is a commonly understood cultural or emotional association that some word or phrase carries, in addition to the word's or phrase's explicit or literal meaning, which is its denotation.
In the end, any difference in meaning is irrelevant because both connotations describe a political philosophy that results in more state control, an ever-encroaching police state, and an unsustainable economic model that ultimately fails and causes much pain and suffering.