History

Yeah it's one of those distortions that seems minor until it suddenly isn't, and hence it's one of the depressing distortions that was unintentional. Molotov describes it better than I can (and I prefer quoting him to describe it, bc he was there, quotes from pages 202-204)

I think [Stalin] made some errors in theory, some of which matter even today. The principle of socialism was not formulated clearly and understandably. But who remembers it?

"From each according to his ability, to each according to his work."

That's right, but not quite right.

All of Khrushchev's errors flowed from this mistake. Marx raised this question, and Lenin confirmed it in his essay "State and Revolution." I know it well. There he wrote that at the final stage of communism the principle will be: "From each according to his ability, to each according to his needs. "

Lenin addresses this in chapter 5, largely by summarizing Marx's criticism of Section 3 of the Gotha Programme, with the main "ability...need" quote being:

The state will be able to wither away completely when society adopts the rule: "From each according to his ability, to each according to his needs", i.e., when people have become so accustomed to observing the fundamental rules of social intercourse and when their labor has become so productive that they will voluntarily work according to their ability.

The original Marx quote being:

In a higher phase of communist society, after the enslaving subordination of the individual to the division of labor, and thereby also the antithesis between mental and physical labor, has vanished; after labor has become not only a means of life but life’s prime desire and necessity; after the productive forces have also increased with the all-round development of the individual, and all the springs of cooperative wealth flow more abundantly, only then can the narrow horizon of bourgeois right be completely transcended and society inscribe on its banners: From each according to his abilities, to each according to his needs!

Molotov's critique of "in the lower stage of communism, in socialism, we have "from each according to their ability, to each according to their work"" continues as follows:

The later formulation has only part of this phrase: "from each according to his ability." But the second part, "to each according to his needs," was replaced by "to each according to his work." Our press follows this line like a law, but it's not correct from a Marxist perspective. Why? First, Marx wrote that only at the final stage of communism could the principle "from each according to his ability, to each according to his needs" be fulfilled. It's logically connected. Why? You can't demand the best from the common laborer under our conditions. But the constitution was written in 1936, when it was impossible to take "from each according to his ability."

They didn't even have housing. Only at a higher stage could you talk about it. Could one demand this of a collective farmer? After all, we have established that he must work a certain minimum number of labor-days. But he is paid only a pittance for these labor-days. If he does not fulfill his quota of labor-days, the kolkhoz has the right to exclude him from membership. So what kind of "according to his ability" is that? It's nothing but window dressing. But window dressing is intolerable in Marxism. Marxism is an objective science; it views things soberly. It calls bad things bad and good things good. It demands genuine, uncompromising struggle for the good. Window dressing is not allowed.

Marx argued, and Lenin confirmed, that the rights of man cannot exceed his economic potential. You can demand that a communist work "according to his ability, " and it doesn't matter what his working conditions are. But you can't demand this from the people. How can we have the same demands under socialism as under communism? Do we create some kind of fiction about something that still does not exist? I wrote a letter to the Central Committee when I was in Mongolia. I said we weren't even demanding this of communists, even though they acknowledged their duty to struggle for communism irrespective of conditions. Revolutionaries must destroy what is bad and sacrifice themselves if necessary. Workers scrape by and receive their crusts of bread-what more can we demand of them?

Meet your quota! That's it. God grant that everyone conscientiously fulfill his norm. We would lead a much richer life. Better yet-exceed one's norm. This applies all the more to communists; a communist must work better. This means that contrary to "from each according to his ability" we must inscribe: fulfillment of the norms established by society. Fulfill what is demanded of you by the state, by society; conscientiously fulfill the norms prescribed by the factory, the workshop, the kolkhoz. This applies especially to white-collar workers. They are so many idlers. As they gossip and smoke in corridors, do you believe they are actually working "according to their ability"? Why do we put up with it? Lenin used to say, we must have factory-style discipline in our workplace. It's not very pleasant, but it's necessary. Factory discipline is not our ideal, but for the present it is indispensable. Honestly, conscientiously, with all your heart, fulfill the norm established by the state. If you exceed your norm, you will be thanked.

Second, "To each according to his work." This is especially popular. All of our books go on about it. Some people interpret it as follows: "if I work in a factory, I am paid according to my work. But if you are a boss, you have no work-norm to fulfill. In a word, you can take all kinds of liberties." Thanks to this scandalous situation, under the guise of "according to one's work," loafers--and they are numerous-get money for nothing.

tldr; So to summarize, Molotov's issue with Stalin's formulation in the 1936 constitution (from...ability, to...work) is that the first part ("from each according to ability") isn't possible given shitty pay in e.g. a collective farm or e.g. lack of housing around a new mine, and the second part ("to each according to work") is demonstrated false by idlers being given equal pay as hard workers. To quote Molotov again because he says this very very well:

It's nothing but window dressing. But window dressing is intolerable in Marxism. Marxism is an objective science; it views things soberly. It calls bad things bad and good things good. It demands genuine, uncompromising struggle for the good. Window dressing is not allowed. ... Here we see young people growing up; honestly they say: this is stupid. What our elders babbled to us does not correspond to reality.

If Molotov were sent back to 1936, as he said above, he would likely tell Stalin to replace "from each according to their ability, to each according to their work" with something like "From each according to the quota, to each according to the wage-scale".