You're talking 'carezzando' touch (jstor)
vs normal (poking). Both may employ arm-weight.
This article requires JSTOR subscription, so I'll quote it here.
Chopin also commanded certain techniques which were relatively uncommon, even in his own time, and which have become increasingly rare as pianism has continued to evolve. One of these is the caressing touch, in which the finger is not lifted directly from the key but rather slides back towards the palm of the hand, which Johann Nikolaus Forkel described in connection with J. S. Bach's clavichord playing, and Frederic Kalkbrenner mentioned in his 1831 piano treatise. This would later be called the carez- zando style.
Chopin's student Wilhelm von Lenz described precisely this kind of touch in the context of a particularly trying lesson on Chopin's Nocturne in C minor, op.48 no.1: [Chopin] was no less exacting when it came to the descend- ing C before the quaver rest at the end of the semiquaver group (fourth bar, third beat); the C was either too short or too long. I found a way out by 'combing' this with the thumb, that is by sliding the finger along the key and releas- ing it only upon reaching the outer edge. This way the end of the phrase at last satisfied him; but that was nothing beside Chopin's own playing ...
The sliding finger said by Jean Kleczyfiski to be used by Chopin, but anathema for years on the piano, was the true eighteenth-century touch for the keyboards of that period, and it was this soft, sliding touch that gave, that still gives, to the old keyboards their charming legato. Modern pianists are quite out of their depth when confronted by instruments of that period. Through the development of piano technique, this touch has become obsolete, and eludes the present-day enthusiasts, who 'dig' for it with the greatest perseverance, and are no nearer the mystery.
It is true, however, that caressing the keys pre-dated Chopin, and it seems that it was largely associated with musicians of the Parisian school. A prime example is Frederic (born Friedrich) Kalkbrenner, one of the most famous and productive students of the first major instructor of piano at the Paris Conservatory, Louis Adam. In his method Kalkbrenner is clear but brief about the touch: " The manner of striking the note must be infinitely varied, according to the different sentiments one wants to express; now caressing the key, now hurling oneself on it like a lion seizing his prey."
The individual who codified the carezzando style had, like Chopin, been reared in a provincial Polish environment, and thus originally schooled in a non- Parisian tradition. Antoine de Kontski (1817-1899), born Anton Kotski in Krakow, was a musical prodigy, and his family (he had four similarly preco- cious siblings) moved to Warsaw when he was six or seven.17 From there, he followed the prodigy's tradi- tional track of performances, teaching and composi- tion, taking lessons with John Field in Moscow (1829-30) and later settling in Paris. ... Kontski's pianism was quiet, like that of Adam, Kalkbrenner and Chopin. Like Kalkbrenner, he felt that one should never play from the arm (that is, the whole arm), and that the forearm should be used only in certain circumstances, such as in playing vigorous chordal passages, or in phrasing 'when one wants to sing, caressing the keys'. Kontski is more explicit about the carezzando touch than any other author (indeed, he seems to have coined the term for it), and it is mostly for this that he is remembered by historians of piano technique. For him, carezzando depended on both finger and forearm; not only did the finger draw inward after striking the key, but the forearm drew back as well.