“Reploids... created by humanity, yet possessing abilities far beyond our own…”
In 21XX AD, Dr. Cain -- the most gifted roboticist of the era (sometimes archeologist, sometimes paleontologist) -- is known to have developed robots containing an innovative new feature - the ability to think, feel and make decisions for themselves, having emotions and sentience. The very first that he developed (who may or may not have been Sigma) was a robot born with the highest abilities, without comparison from all prior robots, and seemed to exhibit limitless strength and intelligence.
Cain named this new type of robot ‘Reploid’ (レプリロイド, Repliroid), seemingly a portmanteau of ‘Replica’ (レプリカ, from replicare: to duplicate) and ‘Android’ (アンドロイド, from Andro-: ἀνδρ, male + -oid: likeness, meaning ‘humanoid robot’) or its shorthand ‘Droid’ (ドロイド, meaning ‘robot’).
This general term is contrasted in 21XX with ‘Mechaniloid’ (メカニロイド, Mechaniroid), a similar portmanteau replacing ‘Replica’ with ‘Mechanical’ (メカニカル, from mēkhanikos: μηχανικος, pertaining to mechanical labor → Mēkhanē: μηχανή, machine). Unlike the Reploids, Mechaniloids are unaware machines that follow set programming.
The Reploids, however, were not Dr. Cain’s original creation. Prior to their development, Cain had unearthed the laboratory of Dr. Light, renowned as The Father of Robotics. Deep therein, he discovered the good doctor’s magnum opus: Mega Man X.
Not simply a robot, X was something totally different that could not be analyzed even by modern science. Dr. Light had made a new type of robot with more complex, human-like mental capabilities. At times, X seemed more like a man than like a machine.
X’s seeming humanity stemmed from a “Distress Circuit”, 苦悩回路, kunō kairo) Dr. Light installed in X’s electronic brain. This circuit -- comparable to Rock’s “Conscience of Justice Circuit” (正義の良心回路, seigi no ryōshin kairo) -- was intended to make robots like X think and “worry” (なやむ, nayamu) like a human, by utilizing their conscience.
Guided by Dr. Light’s design notes -- which were a quantum leap beyond anything the world has ever seen -- Dr. Cain set out to research, analyze and reverse-engineer Mega Man X. Though he didn’t completely understand how all of Dr. Light's systems worked (therefore not all of his functions could be fully analyzed), Cain succeeded in replicating and integrating Dr. Light’s design concept (after a few small revisions to the system) to give birth to what he would later call his first Reploid: a replica of X.Due to the peculiarities of this origin, it is often thought that Mega Man X himself is not a ‘Replica’, thereby X (and his contemporary, Zero) are excluded from being Reploids.
On the other hand, Dr. Light himself always intended for someone like Dr. Cain to carry on his work in a far-flung future, calling X the “first”  of a new generation of robots characterized by their humanity. As robots designed to look like humans, with advanced mental capacities roughly the same as a human’s, any robot with a Distress Circuit (Zero included) would be considered a Reploid.
By this train of thought, rather than Reploids being replicas of X,“they are androids who are replicas of humans”, thereby, Mega Man X is a ‘Replica’ and considered a Reploid.
When to consider X a Reploid and when not to consider X a Reploid? That question has been a point of contention from the very beginning of the X-series.
The concept of X not being a Reploid, despite in-game claim to the contrary, appears to have come from The Journal of Dr. Cain section of the first game’s manual. However, this material did not actually exist within the original Japanese manual. Instead the original contained a different Introduction Story, an extended Warning and main character profiles[8.1].
The Journal of Dr. Cain eventually made its way into the canon through Rozner Labs’ 1995 port of Mega Man X (by Stephen Rozner of DOS Mega Man infamy), when it got translated into Japanese the following year. Materials from the English version were then edited to better fit the story and combined with the Japanese content into one super manual. This edited Journal was also reprinted in 2005’s “Compendium of Rockman X”.
On the Japanese side of things, both X and Zero have always been referred to as Reploids, perhaps due to their unknown origins, though they’ve also been excluded in somewhat equal measure. Note how Gate addresses X and Zero as ‘old robots’ in X6, yet Turtloid calls them ‘Reploids’ still. And note how Cain differentiates X while Zero and Sigma do not.
Overall, there seems to be a lack of proper distinction between the Reploids of 21XX and the humanoid robots of 20XX. Since robots are now divided into only ‘Reploid’ and ‘Mechaniloid’, calling them Mechaniloids wouldn’t be right either.
Now, the rare and ill-defined term ‘Bioroid’ (バイオロイド, from bio- bios, life) is also said to exist in the setting (as seen with Togerics, a mechanized plant from Mega Man X4). Its most notable use comes from the ZERO-series. Namely: the Four Guardians of Neo Arcadia - The ‘Big4 of X-Bioroid.’
As the story goes, having been made using a certain famous Reploid as a base (born from X’s DNA / having X’s Cyber Elves installed) the Four Guardians are considered to be existences above those of normal Reploids. Yet, those same normal Reploids were -- by definition -- based on X as well, each seemingly unable of tapping into the limitless potential they could have inherited from X7].
What the above example nicely highlights is exactly how the developers handle X's connection to his fellow Reploids.
If one focuses on X’s differences to them, he is to be excluded.
Without spoiling much, Rockman X The Novel -Irregulars Report- by Tsubasa Todoroki nicely tackles such ‘hidden setting’ details in all its complexities, taking seemingly incongruent interpretations of the Mega Man X-series and weaving them into a single compelling narrative.