Crystals are the product
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Smooth means many tiny crystals
A smooth fudge is not uncrystallized; it is crystallized into particles too small for the tongue to detect individually. A grainy one has fewer, larger crystals. Same sugar, same water, same cook: different crystal population, produced by what you did while it cooled.
Which is why cooling and agitation matter so much
Crystals need somewhere to start and energy to grow. Agitating a hot syrup gives existing crystals room to grow large; letting it cool undisturbed and then agitating it hard produces an enormous number of tiny ones at once. The instruction to cool before beating is the whole mechanism in one line.
Seed crystals are the enemy until they are the tool
A single sugar crystal on the side of the pan, or an undissolved grain, will seed growth in a supersaturated syrup and produce exactly the coarse structure you were avoiding. Washing down the pan sides is not fussiness; it is removing seed material.
Interfering agents keep crystals small on purpose
Corn syrup, invert sugar, acid, butter and milk solids all get in the way of sucrose crystals forming cleanly, which is why so many recipes contain one. They are not sweeteners doing a flavor job; they are there to control crystal size.
Some products want no crystals at all
A hard candy or a clear brittle is an amorphous glass rather than a crystalline solid, and there any crystallization is failure. That is why the same contamination that ruins a hard candy is deliberately induced in a fudge.
Which makes this the mirror of the syrups property
There, crystals in the bottom of a bottle are a defect caused by finishing above the window. Here they are the point. Same chemistry, opposite intent, and the pages read as mirror images of each other.