Both are a transliteration of Whiskey (uisge beatha–the Gaelic for water of life.)

Hmmm. I think, like Lucasz, I'd need convincing on this one, Helen.

It's a romantic notion that whiskey was the original stuff of life - well, still is , though I'll take the Scotch variety, thanks - yet surely the chilly Northern Europeans would have independently developed their own tipple at around the same time? Giving it a name that's derived from a word for "water" (with a bit of "fire" or "life" thrown in) is natural enough.

Or am I unaware of an established pattern of European migrations in the dim and distant past?

Vodka and whiskey are definitely pretty distinct drinks these days. Vodka is actually far closer to pot(ch)een the potato-based spirit than to whiskey.
Which, incidentally, is highly recommended if you really want to blow your head off, and can get the real thing.