The question has been asked as to whether the Socialist Rule of society ("From each according to his abilities, to each according to his needs") was, in essence, a vision that is equivalent to the Golden Rule ("Do unto others as you would have them do unto you.). The answer is "no." It is, however, a very good question that requires some thought.
There is a fundamental difference between the two Rules which is evident immediately. The Golden Rule is a direction to individuals on how to live. The Golden Rule is a requirement for me to obey, not for me to impose on anyone else. The Golden Rule has no government context at all. It is a direction to free agents to act in a manner consistent with the commands of God. Under the Golden Rule, I must do for others as I would have them do for me. I must live under the Golden Rule without any expectations being placed on anyone else. I have no right, under the Golden Rule, to expect anyone else to do anything for me, I only have a duty to do for them. I cannot, under the Golden Rule, ever take what is someone else's unless I would allow (and actually desire) them to take from me whatever they want to take from me. I must be generous without ever being demanding. I must share with all and demand from none.
The Socialist Rule, by contrast, is entirely a statement of what to expect from others. It is a directive to government (or the state or society) as to how people ought to give to the government or receive from the government. The Socialist Rule begins as a demand from someone to give. "From each according to his abilities." In the Socialist Rule system, we begin not as free agents serving in love, but as servants being commanded. For example, "from each according to his abilities" means that someone must decide what my abilities are and that they would have the right to require me to work in whatever would match my abilities. If the state thinks I would be best as a lawyer, then I must be a lawyer. If the state believes my abilities are best used as a ditch digger, then I must be a ditch digger. My abilities are to be determined by them and I must live by that determination. I have no free agency in this case. It is not "from each according to his love" or "from each according to his desire," but "from each according to his abilities." If the state decides my ability is to be a great tennis player, then I must be a tennis player, even if I hate tennis and would prefer to work among the sick. I cannot choose to do something else, something that is less than my abilities allows in the mind of the authority, without violating the rule.
Secondly, it requires that I be given only what I need. "To each according to his needs" requires that a decision be made about what are my "needs." The person to whom the Socialist Rule is given is to decide what I need and to give me only what I need. The Golden Rule, by contrast, requires its hearer to give me not what he thinks I need, but what he himself would prefer in my place. He is to love me, not just feed me. The Socialist Rule may decide that I "need" only a small apartment and that my neighbor needs a dacha in the woods. In such a case, it must give him a dacha in the woods and give me a small apartment. Under the Golden Rule, I may receive great kindnesses far beyond my needs, but under the Socialist Rule, any such kindness would be deemed to be sin, as someone else would be giving me what is his own "need" and therefore violating the Rule.
The Socialist Rule presupposes a government (or some authority) which has the right to demand from others (from each according to his abilities) and apportion to others (to each according to his needs). The Golden Rule supposes an individual making daily determinations of love for those around him. He will often do something that is not within his best abilities or keep less than is within his needs, both of which would be sin under the Socialist Rule.
The Golden Rule is a rule for individuals who live freely under the God of all things, serving Him by serving others. They do what is best for others, not themselves. They give what is best for others, not based on need but on love.
The Socialist Rule is a rule for government, under which freedom is replaced by "ability determinations" and under which rewards are neither from God nor from man, but based purely on needs.
The Golden Rule is a glorious standard for a relationship of love. The Socialist Rule is a mechanistic standard for imposition of duties and restrictions on possessions.
And, of course, I would note that the two cannot coexist. A man who is limited to working according to his "abilities" cannot choose to act in love if it requires him to do other than his abilities. A man who has only what he needs will be hard-pressed to provide to others any gift of love.
Finally, of course, we have seen that the Socialist Rule, where it is embraced, is a failure. The result, as we who hold to Christianity would expect, is that many do not act "according to their abilities" but according to their natural loves (for their children and family and friends) and assign tasks and jobs based on relationships, not abilities. We also see that they obtain goods not because of needs, but because of their desires (dachas, cars, servants). A mechanistic test applied in a manner not driven by love, but by abilities and needs, cannot work in a world of fallen man.
It is conceivable that a society built on the Golden Rule might, in many ways, be similar to a society built on the Socialist Rule, if the Socialist Rule is applied in a truly Communistic (scientific socialism) basis, where there is no government at all to make decisions about abilities and needs. But it is difficult to imagine how a society built on the Socialist Rule can be anything but an authoritarian society, given its command to "take" and to "give" from and to each individual. A society built on the Golden Rule can never be an authoritarian society because it denies that anyone has any authority over an individual's act of love.
Under the Golden Rule, my only authority is God. I give not according to my abilities (however we define it), but according to my love. I receive, from others, not according to my needs, but according to their love.
And God receives the glory.