Fudge and barfi arrive at a similar place: a firm, sliceable, dairy-rich sweet whose texture depends on very small sugar crystals. The routes there differ, and the differences are instructive.
Both depend on controlling crystal size
A sugar solution cooled past saturation will crystallize. Whether the result is smooth or gritty depends entirely on whether many small crystals form or a few large ones.
Smooth texture requires many nucleation points forming at once, so no individual crystal has room to grow large enough for the tongue to detect.
Everything both confections do procedurally is aimed at that outcome, which is why their failure modes are identical even though their methods are not.
Fudge controls crystals through cooling and agitation
Fudge is boiled to a specific concentration, then cooled without disturbance to a much lower temperature before being beaten hard.
Cooling undisturbed keeps the solution supersaturated, and the sudden beating then triggers crystallization everywhere at once, producing the fine grain the sweet is judged on.
Beat it while still hot and the crystals grow coarse, which is the classic fudge failure and the reason the method is so specific about temperature.
Barfi controls crystals through solids and stirring
Barfi carries a much higher proportion of milk solids, nut flour or coconut, and those particles physically obstruct crystal growth.
Continuous stirring during cooking rather than a single beating stage distributes nucleation through the process, so crystals stay small without a separate cooling step.
The mixture is then poured while hot and left to set, which works because the solids are already doing the job that fudge achieves through timing.
The ingredient lists reflect the two strategies
Fudge is mostly sugar with dairy and fat, so the sugar chemistry dominates and the procedure has to be exact.
Barfi is closer to equal parts solids and sugar, which makes it far more tolerant of imprecision but also denser and less sweet on the palate.
A cook moving between them will find barfi more forgiving of technique and less forgiving of ingredient quality, since the solids carry the flavor directly.
Interference agents appear in both traditions
Fudge recipes add corn syrup or an acid, both of which disrupt the crystal lattice and keep the texture smooth over time.
Barfi achieves the same effect with milk solids and ghee, and where a recipe wants an especially soft set it adds cream or condensed milk.
Two traditions, no contact for most of their history, arrived at the same principle: interrupt the crystal, and the sweet stays smooth.