How is Qur'an 4:93 (which forbids killing a believer) compatible with the death penalty?

Question

But whoever kills a believer intentionally - his recompense is Hell, wherein he will abide eternally, and Allah has become angry with him and has cursed him and has prepared for him a great punishment. -- Qur'an 4:93

However, under sharia law, Muslims may be executed for e.g. murder, adultery, apostasy, sodomy (see this question), and this is stipulated in the Qur'an (qisas):

O you who have believed, prescribed for you is legal retribution for those murdered ... -- Qur'an 2:178

Thus, sharia literally includes killing a believer intentionally, which raises the question as how this fits in with Qur'an 4:93.

Question: How is Qur'an 4:93 compatible with the death penalty?

The only way to reconcile this I can think of is that the scope of Qur'an 4:93 is limited to murder (unjust killing) of a believer. If that's correct, I'd like an authoritative reference to back up this guess.

A tafsir indicates Qur'an 4:93 was revealed in light of Miqyas Ibn Sababah whose brother was murdered; the murderer could not be found, so Miqyas killed an emissary sent by the Prophet. (The Prophet subsequently sentenced Miqyas to death, but regarded him as having left Islam.) This is consistent with the idea that the scope of Qur'an 4:93 is limited to murder.

Answer 1

It is true as you mentioned that it forbids killing believers ... but this verse can be related to common situation (about believers, and has not mentioned the exceptions and actually is deemed as a general issue), and in truth it is not related/mention the ones who do specific activities that are horrible haram activities (whose punishments are execution ...).

In order to see more related explanation about the commentary of that, you can read the text below:

Commentary, QUR'AN:

And it does not behoove a believer to kill a believer except by mistake: al-Khata' (mistake) has no elongation; to read it with elongation (al-khata') is wrong; here it gives a meaning opposite of 'intentionally', as the following verse (And whoever kills a believer intentionally...) shows. "It does not behoove" in this verse denotes negation of demand or requisition.

In other words, it says: When a believer enters the sanctuary of faith and belief, there remains in him nothing to demand the killing of another believer who like himself is within the same sanctuary, except if it happens without his intention. Thus the exception is joined, not isolated. The meaning in simple words is as follows: A believer does not want to kill a believer, per se; he cannot think of killing him knowing that he too is a believer. There are other verses like this sentence in the same style and the same negation of requisition. For a example: ...

To see the rest of the text (commentary), kindly refer to this reference.