We speak about fornication if there is an unlawful sexual relationship between a man and a woman where marriage is not present in each case. It is important to note that neither of them is married to a third person. This is “Zani”, the one who commits fornication:

The woman and the man guilty of adultery or fornication, - flog each of them with a hundred stripes: Let not compassion move you in their case, in a matter prescribed by Allah, if ye believe in Allah and the Last Day: and let a party of the Believers witness their punishment. (Quran 24:2)

Zina includes sexual intercourse between a man and a woman not married to each other. It therefore applies both to adultery (which implies that one or both of the parties are married to a person or persons other than the ones concerned) and to fornication, which, in its strict signification, implies that both parties are unmarried. The law of marriage and divorce is made easy in Islam, so that there may be the less temptation for intercourse outside the well-defined incidents of marriage. This makes for greater self-respect for both man and woman. Other sex offences are also punishable, but this Section applies strictly to Zina as above defined. [Although Zina covers both fornication and adultery, in the opinion of Muslim justice, the punishment laid down here applies only to un-married persons. As for married persons, their punishment, according to the Sunnah of the Prophet (peace be on him), is stoning to death. Remember that this jurisprudence was applied in Medina 1400 years ago, so it was tailored to the ancient community of Medina. It is not the judgment itself that has to be taken literally, but the logic. Judgment and jurisprudence depend on age and place and follow the norms of the given community.

The punishment does not stop here:

Let no man guilty of adultery or fornication marry and but a woman similarly guilty, or an Unbeliever: nor let any but such a man or an Unbeliever marry such a woman: to the Believers such a thing is forbidden. (Quran 24:3)

From here, let's review the case of adulterers. They are those who live in a marriage relationship and commit sexual act with a third person. We are speaking exclusively about woman and man:

And those who launch a charge against chaste women, and produce not four witnesses (to support their allegations),- flog them with eighty stripes; and reject their evidence ever after: for such men are wicked transgressors;- (Quran 24:4)

The most serious notice is taken of people who put forward slanders or scandalous suggestions about women without adequate evidence. If anything is said against a woman's chastity, it should be supported by evidence twice as strong as would ordinarily be required for business transactions, or even in murder cases. That is, four witnesses would be required instead of two. Failing such preponderating evidence, the slanderer should himself be treated as a wicked transgressor and punished with eighty stripes. Not only would he be subjected to this disgraceful form of punishment, but he would be deprived of the citizen's right of giving evidence in all matters unless he repents and reforms, in which case he can be readmitted to be a competent witness.

Unless they repent thereafter and mend (their conduct); for Allah is Oft- Forgiving, Most Merciful. (Quran 24:5)

And for those who launch a charge against their spouses, and have (in support) no evidence but their own,- their solitary evidence (can be received) if they bear witness four times (with an oath) by Allah that they are solemnly telling the truth; (Quran 24:6)

The case of married persons is different from that of outsiders. If one of them accuses the other of unchastity, the accusation partly reflects on the accuser as well. Moreover, the link which unites married people, even where differences supervene, is sure to act as a steadying influence against the concoction of false charges of unchastity particularly where divorce is allowed (as in Islam) for reasons other than unchastity. Suppose a husband catches a wife in adultery. In the nature of things four witnesses - or even one outside witness - would be impossible. Yet after such an experience it is against human nature that he can live a normal married life. The matter is then left to the honour of the two spouses. If the husband can solemnly swear four times to the fact, and in addition invoke a curse on himself if he lies, that is prima facie evidence of the wife's guilt. But if the wife swears similarly four times and similarly invokes a curse on herself, she is in law acquitted of the guilt. If she does not take this step, the charge is held proved and the punishment follows. In either case the marriage is dissolved, as it is against human nature that the parties can live together happily after such an incident.

And the fifth (oath) (should be) that they solemnly invoke the curse of Allah on themselves if they tell a lie. (Quran 24:7)

But it would avert the punishment from the wife, if she bears witness four times (with an oath) By Allah, that (her husband) is telling a lie; (Quran 24:8)

And the fifth (oath) should be that she solemnly invokes the wrath of Allah on herself if (her accuser) is telling the truth. (Quran 24:9)

In the above ayas, only the sanction is mentioned where an outsider slanders a decent woman. If he does not come up with four witnesses, his act should be punished by eighty stripes. We often hear that four independent witnesses need to prove adultery. If that was the case, proof would still be practically impossible. But we have argued earlier that the four witnesses prescribed in the Quran are not for adultery, but for proving homosexuality and lesbianism. Ayas regarding adultery do not even mention the worldly punishment. We can read only about the afterlife punishment. See details above. If the spouse suspects his/her partner with adultery, he/she has to take an oath four times. If he/she swears the fifth time, he/she calls for the curse of Allah. This means that if he/she is right, the perpetrator will go to hell, if he/she sworn falsely he/she will go to hell. Other worldly punishment is entrusted by the Quran to the community, which judges according to the cultural level and norms of that age and place.

Narrated 'Abdullah bin Mas'ud: that the Messenger of Allah (peace be upon him) said: "The blood of a Muslim man, who testifies that none has the right to be worshipped Allah, is not lawful except for one of three cases: The (previously married or) married adulterer, a life for a life, and the one who leaves the religion and parts from the Jama'ah (the community of Muslims.)

Book: The Book on Blood Money
Grade: Sahih (Darussalam)
Reference: Jami` at-Tirmidhi 1402
In-book reference: Book 16, Hadith 18

This hadith sets up the logic that is represented by the Islam. I am not talking about judgment, but about the logic. Because it's about betrayal. Marriage is a sort of belonging to a small community that ensures succession. Respect the sanctity of life is the foundation of belonging to any community. The betrayal of faith or community in Medina meant high treason, for the Islamic State was based on faith and law. Thus, the derivation ends up with betrayal.
Now I could quote a lot of other Hadith about the sentence of this deed by stoning, execution but I don't do that. I have already done this when dealing with homosexuality and lesbianism. Then, compared the Hadith to the Quran, the outcome became different. The Quran does not open the door of the concrete legal sentences and also raises the idea of repentance and forgiveness which does not appear in human judgments. Following Islam, we have to decide whether we want participate in a time-travel back to the past or we should transpose the logic and spirit of Quran into the present. I profess the latter one, so I'll stop here in this case.