Assassination is not a term possessing a hyper-technical definition that requires someone to be a member of the victim's own party or nation or anything else. The most common definitions have as their main element that the attack is "treacherous." It doesn't matter who the target is or who the assassin is, or whether the target's death is a good or bad thing. It is the manner in which the attack is carried out. Had Hitler died in the bomb blast at the Wolf's Lair, the world would have rejoiced, but it still would have been an assassination. Likewise, had Dahlgren succeeded in penetrating the Richmond defenses, fought his way into the White House of the Confederacy and killed Davis, it would have been a surprise attack - had he and his men been in civilian clothes or Confederate uniforms, it would have been an assassination. While there was no Executive Order in 1865, there was International Law, which clearly condemned assassination.
From Vattel's "The Law of Nations" (1852): I give, then, the name of assassination to a treacherous murder whether the perpetrators of the deed be subjects of the party whom we cause to be assassinated, or of our own sovereign,—or that it be executed by the hand of any other emissary, introducing himself as a supplicant, a refugee, a deserter, or, in fine, as a stranger; and such an attempt, I say, is infamous and execrable, both in him who executes and in him who commands it.
From "Black's Law Dictionary" (1910): ASSASSINATION. Murder committed for hire, without provocation or cause of resentment given to the murderer by the' person upon whom the crime is committed. Ersk. Inst. 4, 4, 45. A murder committed treacherously, or by stealth or surprise, or by lying in wait.
From "Bouvier's Law Dictionary," Revised 6th Ed (1856): ASSASSIN, crim, law. An assassin is one who attacks another either traitorously, or with the advantage of arms or place) or of a number of persons who support him, and kills his victim. This being done with malice, aforethought, is murder. The term assassin is but little used in the common law, it is borrowed from the civil law.
Also note that Jefferson Davis refers to it as assassination in Vol. II of his "Rise and Fall of the Confederate Government."
Arguably the most famous assassination was that of Julius Caesar by Brutus & Co.