The smoke does not come from the still or the cask. It is introduced during kilning — the drying of the germinated barley — and the damp grain takes up the phenols from the smoke passing through it. This is why the level of peating is fixed before fermentation has even begun.
What PPM actually measures
Peating level is quoted as phenol parts per million, and the figure almost always refers to the MALT, not the finished spirit. A great deal is lost through mashing, fermentation and distillation, so the phenol content of what reaches the bottle is markedly lower than the number on the marketing material. Two whiskies quoting the same malt PPM can arrive at quite different intensities.
Why regional peat differs
Peat is made of whatever grew and decayed in that bog. Coastal peat, Islay's especially, contains more marine and seaweed-derived material than inland moorland peat, and that is the usual explanation offered for the iodine, brine and tar characters associated with the island. The association is strong; the causal chain is less firmly established than it is usually stated to be.
Not all Scotch is peated
Peating is a choice, and most Scotch made today is unpeated or only lightly so. It became a regional signature rather than a national one.