The SR4 errata don't cover this point. I would say that the spell's damage listing is correct; the lightning combat spells should do physical damage; but, also apply the electricity effect rules for incapacitating the target, applying negative modifiers, etc., as with a shock glove or taser.
Let me start by saying that I don't know any official citation that gives a reason for stun being more draining than lethal damage. But I know what happened in sr4 in my group and that sheds light on a list of valid reasons why they might have done it:
In sr4, spells doing stun damage were cheaper on the caster than spells doing real damage. However, a person that is completely stunned in a combat is just as dead as a person that is really dead. Because killing a stunned target is basically a free non-combat action without cost. If not getting enough damage to be out of the fight instantly, you get modifiers. But it does not matter if it was stun or real damage. The modifiers are always the same. So:
- to stun somebody, you would prefer to do enough stun damage.
- to kill somebody, you would prefer to do enough stun damage and later kill him trivially with a knife or firearm
Going for real damage only made sense in combination with other damage sources that did lethal damage so it would add up to an amount ending the fight. A well optimized caster could take out people without such a use of combined arms however. So for a well optimized caster, using the cheaper stun powers for killing was the economically viable choice.
So my guess is that the more powerful spell (choice between stun and stunned and later killed anyway compared to always killed) was made more costly than it's lethal counterpart so people intending to kill actually use the deadly spell for this purpose.
Considering in-game justifications for the mechanics, at first glance it seems odd because killing is more powerful and should be more taxing on the caster. But one could argue that the drain actually takes it's toll from the amount of control you have to assert and killing someone outright requires little control while managing the exactly right amount to stun somebody requires a lot of control over the magical energy used.
Best Answer
Rules for designing a new spell appear in Street Magic, pp. 158-162.
A couple of excerpts:
A Combat spell has a Threshold of 12, and a 3-month Interval. There are various conditional modifiers in the table that may apply.
If you copy existing spell stats, I think the cost should come out to be the same. You will want to use the 'Ice' elemental effect (p. 164):
The formula may exist on the Matrix or elsewhere; that would be at the GM's discretion.