What Exactly is the Meaning of "Fatal"?

Fatal does indeed derive from the same root as fate according to the online etymological dictionary. The original meaning "belonging to or appointed by fate" is still valid if rare according to Chambers, but seems to have mostly taken on the darker, doom-laden shades of fate.

Fateful is a different adjective deriving from fate. It means "charged with fate" (i.e. full of fate/doom, the usual result of tacking on the suffix -ful) rather than "possessing the qualities of fate" (the usual result of tacking on -al).

To complete the set of adjectives, let's not forget fated. It's a perfectly good doom-laden word, after all.

This is an interesting question. Fatal originates from Latin fatalis, meaning something like pertaining to fate. It is not so deadly, per se, but then if we examine what fate means, things become a little clearer:

• something that unavoidably befalls a person; fortune; lot
• the universal principle or ultimate agency by which the order of things is presumably prescribed; the decreed cause of events; time.
• that which is inevitably predetermined; destiny: Death is our ineluctable fate.

So it makes sense that fatal and fate are connected, since death is the ultimate fate of all living things.

Now fateful on the other hand, is also from the same root, but the -ful changes the meaning from something like pertaining to fate to something like characterized by fate. In other words, rather than representing our ultimate destiny, fateful describes something that has some sort of significance with regard to our fate. So fateful is not as deadly as fatal because it contributes to or furthers us toward our fate, rather than being our fate.

Could "fatal" be a variant of "fateful," perhaps with the "deadly" connotations alluded to above?

Yes, which is emphasized by the fact that one of the rarer meanings of 'fatal' is 'decisively important; fateful'. In fact, it's the other way round: 'fateful' (1705–1715) is actually formed from 'fate' (1325–1375), which shares a similar heritage with 'fatal' (1350–1400); namely, the Latin 'fātālis' which unsurprisingly means 'of fate'.

As something which terminates life is to be that life's ultimate end, or fate, the word 'fatal', understandably, often describes that which causes the termination to occur.

You're right about the etymology - from the Online Etymological Dict.:

late 14c., "decreed by fate," from M.Fr. fatal (14c.) and directly from L. fatalis "ordained by fate," from fatum (see fate); sense of "causing death" is early 15c.

Going a bit further back, we might look at the ancient Greek Moirai - the three Fates:

Klotho combs the wool and spins the thread of life.

Atropos weaves the thread into the fabric of one's actions.

Lachesis determines the length of the thread and thus the period of one's life.

And this classical conception of fate thus sees one's life as a coherent whole, a totality, and from there it's a skip and jump to mortality in a general sense.