The short answer is that spies were treated differently because they were claiming not to be soldiers.
The differing treatment between spies (subject to trial and possible execution) and authorised belligerents (mostly uniformed soldiers) who cannot be killed after capture or surrender, arose from developments in international law aimed at limiting the effects of war and particularly in protecting civilians and limiting the effects of warfare.
The major modern laws of war derive in large part from the Brussels Declaration concerning the Laws and Customs of War 1874, which was a draft submitted by the Emperor of Russia to delegates from a number of European countries. It was not binding on the participants but formed the basis of subsequent conventions and treaties like the Oxford Laws of War on Land 1880, and later Hague and Geneva conventions.
A continuous theme is that civilians are outside the fighting. The targets of war are the opposing belligerents and they can only be killed or wounded until they are captured or surrender, at which time there are a set of rules about how they can be treated. It isn’t just uniformed versus non-uniformed. There is a range of non-uniformed personnel who are entitled to be treated as belligerants, such as sutlers, journalists, and residents of an invaded country who spontaneously take up arms etc. Having said this, the surest way to be classed as a belligerent is to wear the appropriate uniform or military insignia.
Spies have the right to a trial, but under the law of the capturing force. There is care taken to define what a spy is, but the main reason for the different treatment is that a spy is pretending to be a civilian. By deceit s/he is carrying out military activities while pretending to be a protected class of person and this undermines the laws of war which depend on being able to identify whether you are looking at a belligerent or a civilian.
Ref:
https://www.icrc.org/ihl/INTRO/135