Praise be to Allah.
Whoever is killed for the sake of Allah is a martyr. What is meant by “for the sake of Allah” is that he is fighting so that the word of Allah will be uppermost. This is the definition of the martyr killed in battle, as stated by the Prophet (peace and blessings of Allah be upon him).
Al-Bukhari (3126) and Muslim (1904) narrated that Abu Moosa al-Ash’ari (may Allah be pleased with him) said: A Bedouin said to the Prophet (peace and blessings of Allah be upon him), “A man fights for the sake of booty, and a man fights so that he will become famous, and a man fights to show off – who is fighting for the sake of Allah?” He said, “The one who fights so that the word of Allah will be uppermost is the one who is fighting for the sake of Allah.”
Muslim (1915) narrated that Abu Hurayrah said: The Messenger of Allah (peace and blessings of Allah be upon him) said: “Who do you think is a martyr among you?” They said, “O Messenger of Allah, the one who is killed for the sake of Allah is a martyr,” He said, “The martyrs of my ummah would be few in that case.” They said, “Then who are they, O Messenger of Allah?” He said: “The one who is killed for the sake of Allah is a martyr; the one who dies for the sake of Allah is a martyr; the one who dies of the plague is a martyr; the one who dies of a stomach disease is a martyr; and the one who drowns is a martyr.”
So the Prophet (peace and blessings of Allah be upon him) mentioned both the martyrs who die in battle and those who also share the virtue of martyrdom.
Al-Nawawi (may Allah have mercy on him) said: The scholars said: What is meant by the martyrdom of these people who are not killed for the sake of Allah is that in the Hereafter they will have the reward of martyrdom, but in this world their bodies should be washed and the funeral prayer should be offered for them. We have already discussed this in Kitab al-Eeman. The martyrs are of three types: the martyr in this world and the Hereafter, who is the one who is killed in war against the kuffar; the martyr in the Hereafter, who is not treated as a martyr as far as rulings in this world are concerned, who are the people mentioned here; and the martyr in this world who is not regarded as a martyr in the Hereafter, which is the person who steals from the war booty or who is killed when running away from the battlefield.
Martyrdom is a high status, which can only be attained by the believers (Muslims).
With regard to the one who heard the call of the Prophet Muhammad (peace and blessings of Allah be upon him) and did not believe in him, he is a kafir who disbelieves in Allah and is one of the people of Hell, whether he was killed in battle or died in his bed, whether he was a Jew or a Christian or any other religion of shirk and kufr. The Christians are kafirs because they reject the Prophet (peace and blessings of Allah be upon him) and because they claim that the Messiah ‘Eesa ibn Maryam (Jesus the son of Mary) is divine, and because they claim that God has taken a wife and a son – exalted be Allah far above what they say.
Allah says (interpretation of the meaning):
“Indeed, those who disbelieve in Allah and His messengers and wish to discriminate between Allah and His messengers and say, "We believe in some and disbelieve in others," and wish to adopt a way in between - Those are the disbelievers, truly. And We have prepared for the disbelievers a humiliating punishment.”
“The Jews say, "Ezra is the son of Allah "; and the Christians say, "The Messiah is the son of Allah ." That is their statement from their mouths; they imitate the saying of those who disbelieved [before them]. May Allah destroy them; how are they deluded?”
“They have certainly disbelieved who say, " Allah is the Messiah, the son of Mary" while the Messiah has said, "O Children of Israel, worship Allah, my Lord and your Lord." Indeed, he who associates others with Allah - Allah has forbidden him Paradise, and his refuge is the Fire. And there are not for the wrongdoers any helpers.”
“They have certainly disbelieved who say, " Allah is the third of three." And there is no god except one God. And if they do not desist from what they are saying, there will surely afflict the disbelievers among them a painful punishment.”
And the Prophet (peace and blessings of Allah be upon him) said: “By the One in Whose hand is the soul of Muhammad, no one of this nation, Jew or Christian, hears of me then dies without having believed in that with which I was sent, but he will be one of the people of Hell.” Narrated by Muslim, 153.
The above comments have to do with the rulings on his situation in the Hereafter if he is killed. With regard to the rulings on his situation in this world, if a non-Muslim joins the fight to defend a Muslim country without that involving any compromise on religious matters on the Muslims’ part, then there is nothing wrong with thanking him and rewarding him for that.
And Allah knows best.