The Fate series has an absurd amount of characters ranging from historical icons to legendary figures of folklore to even fictional characters that have persisted in the zeitgeist. However, it seems the creators believe the simplest solution is the correct one, and Saber (AKA Artoria Pendragon) has so many lookalikes that each new character bearing a resemblance to her is referred to as a Saberface.
The term first popped up around 2015 in the parody manga Fate/GUDAGUDA Order, funnily enough in reference to a character who - surprisingly - didn't have Saber's face. But this trend has persisted in Fate media since long before this manga, so where did it start, what qualifies as a Saberface, and how did it become the meme it is remembered as today?
Origin of the Saberface
The earliest examples of Saberfaces are conveniently some of the most popular, but also the ones that make the most sense in context, without being swarmed with different variations. According to the wiki, the first was Mordred, the son of King Arthur, who in Fate lore is also a woman in truth much like her father Artoria (it gets a bit confusing).
She was revealed in the 2006 collection Character Material which - as the title suggests - had character materials from various Type-Moon properties. Mordred bearing a resemblance to Artoria makes perfect enough sense from a character design standpoint, making it easy to tell that the two are related.
In the same year that Mordred was unveiled, Gen Urobuchi wrote Fate/Zero and included a plot where Gilles De Rais, the Caster Servant, mistook Artoria for Jeanne D'arc. There was no design for Jeanne at the time, but by the time the anime was released in 2010, the canceled Fate/Apocrypha online game yielded the design that would be teased in the show.
Signs of the Saberface
Those two on their own are pretty excusable and aren't anything egregious so far as character designs go. One is a blood relative and the other was a coincidental lookalike that was part of a character arc, but as the years went on, more characters were created as almost mirrors of Artoria for much less justification.
Some are fairly easy to spot by the hairstyle alone, which tend to have side-swept bangs in some variation, usually a different color or the general direction of the hair's flow. Even when the hair is fairly distinct the cowlick atop her head is a dead giveaway that the character in question is a Saberface.
And other times, it's as simple as the shape of the eyes and general expression, though this is more of a signifier of Takashi Takeuchi's art style having a distinct style with overlap. Things like the nuances between eyes or neutral emotions are what differentiate them, but when the variables overlap, that's how you know you have a Saberface.
Rise of the Saberface
As Fate/Grand Order has taken the world by storm, designs and characters from almost every story in the franchise have turned into collectibles, which has made the trend that much more obvious. When all the alternate takes on Artoria are laid out in front of you, it can be pretty funny to see just how many times storytellers had a new idea on how to put a spin on her design.
But the Saberface wouldn't have persisted at all were it not for Takashi Takeuchi having continued to draw her in myriad ways, both out of love for the character and the meme. Takeuchi even once joked that his Noble Phantasm was called "Unlimited King of Knights" in reference to this great trend.
The meme even has impacted the gameplay of Fate/Grand Order, as some characters will target Saberfaces exclusively or do more damage to them with certain attacks. The meme has transcended mere aesthetics to the point that it is almost a tradition within the franchise, like a role in theater.
There are still variants being created that parody Saberfaces or that attempt to mirror her appearance to the benefit of storytelling. For instance, Gray from Lord El Melloi II's Case Files is a Saberface, though she wasn't born looking like her, and thus hides her face from El Melloi because Saber's face reminds him of the events of Fate/Zero.
Some trends persist long enough to become memes and some memes persist long enough to become more than just running jokes. That isn't to say that it can't still be funny to some or aggravating to others. Regardless, it goes to show that no matter how many different characters appear in Fate, there will always be this lingering desire to put Artoria front and center.