Some history of firearms for those who are curious:
The earliest personal firearm was the hand cannon or gonne. The oldest surviving firearm is a 7.8 pound bronze hand cannon excavated in Banlachengzi (China) in the 1970s, and was manufactured in 1288 or earlier (it was used in a battle there in either 1287 or 1288). There are some earlier recorded uses of these weapons, including the Battle of Ain Jalut in 1260, when the Mamluk Sultanate stopped a Mongol invasion between Acre and Jerusalem with the aid of hand cannon. (Note: This is around 150 years before full plate armor was used, so hand cannon are as medieval as plate armor)
A hand cannon was essentially a metal tube on a stick. Pour in some powder, drop in rocks or an arrow with a leather plug or an iron ball, then light off the powder with a smoldering piece of wood, slowmatch, or a hot iron. It was either wielded with a two man team (a holder and a firer), or one person with a forked stick to balance the hand cannon. It was weak and inaccurate (the weakness due to using mealed powder, the inaccuracy because it was a smoothbore), but it required less training than a bow and less strength (or fiddly mechanical cocking devices) than a crossbow.
The first dated illustration of a developed matchlock occurs in 1475. The matchlock was a slightly refined firearm. It was the first weapon to have the three distinct components of modern longarms – the lock (the firing mechanism), the stock (a means of bracing the firearm against the firer's body), and the barrel (the container of the gunpowder and ammunition, and the director of the force of the weapon). The lock consisted of an s-shaped bar called a serpentine. One end was manipulated by the user, while the other end held a smoldering slowmatch (hemp or flax cord soaked in potassium nitrate), which was lowered into a pan of powder; that pan was under a hole in the barrel that led to the main gunpowder charge, detonating the charge (if all went well). The matchlock was incredibly vulnerable to poor weather. The match also glowed in the dark and gave off a distinct smell, both of which reduced the ability to remain concealed with the weapon. The match also got used up quickly – it was estimated that a single night watchman would use a mile of slowmatch over the course of a year. And of course, there's always a danger from having a smoldering match near gunpowder.
The observant will note I mentioned 1475 being for the “developed” matchlock. There is an illustration of a hand cannon with a serpentine in 1411, apparently a transitional type from the original hand cannon to the more developed matchlock.
There were some interesting variations on the matchlock. In the Palazzo Ducale in Venice, there is a triple-barreled matchlock revolving firearm, about 21 inches long with 12 inch barrels, with a caliber of 11mm. It weighs 3.5 pounds, making it one of the earliest revolving firearms (of the “pepperbox” type) developed (circa 1540). The Luigi Marzoli Museum in Brescia has a triple-barreled arquebus from 1550, which weighs 10 pounds, is 33 inches long with 20.5 inch barrels, and has a caliber of 11.5mm. There's a German 8-shot revolving arquebus with a single barrel in the Germanisches Nationalmuseum Nürnberg that dates to the 1580s, although I haven't found as much information on that one.
While the matchlock was easier to use than the hand cannon, it still had the flaws associated with the lit match. Looking for ways to shoot in worse weather and have less chance of accidentally blowing one's self up, the wheel-lock was invented around 1500. It used a steel wheel that had a spring, which spun against a piece of pyrite to create sparks. Pyrite was preferred over flint because it causes less damage to the steel. The wheel was wound up using a wrench-like device that engaged a square in the middle of the wheel. When the trigger was pulled, the wheel would begin spinning, the pan cover would open, and then a lever with the pyrite would drop onto the wheel (if it dropped first, the spring would need to be much stronger to spin the wheel). White-hot fragments of pyrite would be generated in the pan, igniting the powder. The wheel-lock was (compared to the matchlock) expensive and difficult to maintain, but safer, concealable, and able to be carried around without an inconvenient smoldering match. Also, the covered pan made it more weather-resistant.
The various forms of flintlock began their development in the 1540s, and used flint dropping onto a piece of steel to create sparks (hot pieces of steel) that would fall into the pan. Early snaplocks and snaphaunces had pan covers separate from the steel (the snaplock's cover had to be manually opened, while the snaphaunce's was opened by pulling the trigger), but around 1600 the frizzen (a combined steel/pan cover) was developed, and the true flintlock was born. They were mechanically simpler than the wheel-lock, and quickly became almost universally used (with the exceptions being places where the technology was not introduced, such as parts of Africa or Japan, and weird showpieces like the multi-shot matchlocks I mentioned above).
What's this all mean for someone using Guns of War? Honestly, whatever you want it to. It's just a history of what happened on Earth. In your world, maybe nobody hits on the idea of using springs with guns, so matchlocks stay as the most advanced firearms for centuries. Maybe flint's really rare but pyrite isn't, so wheel-locks stick around longer as the guns of the elite. Possibly everyone is bad at chemistry, and slowmatch isn't developed, so the hand cannon is as far as firearms technology advances.