Tempering, and the crystal forms of cocoa butter
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Why chocolate is different from everything else here
Most fats set one way. Cocoa butter is polymorphic, meaning it can solidify into several distinct crystal structures with different melting points and different appearances. The desirable one gives gloss, a clean snap and a product that releases from a mold and keeps its surface.
What tempering actually does
It is a controlled sequence of temperatures: melt fully to erase all existing crystal structure, cool to encourage the right form to start, then warm slightly to melt off the unwanted forms while leaving the right ones as seeds. Those seeds then propagate through the batch as it sets.
Seeding is the shortcut and it is legitimate
Adding a quantity of already-tempered chocolate to a melted batch introduces the correct crystals directly. It is simpler than working the full temperature curve and it is what many small operations do, and it still requires holding the right temperature afterwards.
Untempered chocolate fails visibly
Dull, streaky, soft, slow to set, difficult to unmold, and prone to bloom within days. Those are all one failure wearing different faces, and they are visible to a buyer immediately, which is why this is the defining skill of the chocolate half of the craft.
The temperatures differ by chocolate type
Dark, milk and white each have their own working ranges, because the milk fat and the different cocoa butter content change the behavior. Using a dark chocolate curve on white chocolate is a common way to produce a batch that never sets properly.
Which is why it is a written procedure
Temperatures, holding times and the test you use to confirm temper before committing a batch. A smear on a knife that sets glossy within a few minutes is the standard check, and doing it every time costs almost nothing against the cost of molding an untempered batch.