Among the chosen examples you can tell the closest-to-ceratopsids apart from the most basal kinds by simply reading their names: the former have usually the suffix -ceratops (ex. Leptoceratops, Zuniceratops), the latter usually end in other ways (ex. Psittacosaurus, Yinlong).
Together with Protoceratops, Psittacosaurus is by far the most important and well-known ceratopsid predecessor. At least, if you ask paleontologists and paleo-fans. Rule of Cool always wins in pop-culture, with small-sized dinosaurs usually with very few chances to get consideration by writers or film-makers - points minus when they are plant-eaters.
Digression closed, here we have many things to say about Psittacosaurus, definitively one of the most important dinosaurs. An Asian animal like Protoceratops it has classically been considered the most ancient ceratopsian ever (lived 100 million years ago, in the Early Cretaceous) and the forerunner of all the Late Cretaceous “neoceratopsians” (aka Proto+Horned). With its primitiveness, Psittacosaurus resembles anything but a Triceratops: small (6 ft long), slender, with only hints of horns and frill. Once thought to be capable of walking on all fours, detailed study of its forelimbs shows it was entirely bipedal. The main trait revealing its relationship with Triceratops is the parrot-like bill (the hallmark of all ceratopsians) which gives it the name “Psittacosaurus” (“psittacos” is Greek for parrot). Another thing which ties Psittacosaurus with its horned descendants are the prominent bony “cheeks”.
Psittacosaurus was discovered in the 1920s in Mongolia together with Protoceratops. Its discovered was famed paleontologist Roy Chapman Andrews – a very adventure-loving guy, to the point he could have even been the inspiration for Indiana Jones. Since then, psittacosaurs have been discovered everywhere in eastern Asia, but recognized a basal ceratopsian only in the 1970s (it was believed an ornithopod before). Its fossil record is extremely rich, just the same level of Protoceratops - individuals from all ages are known, and also several nests full of eggs. Our “parrot-dinosaur” also detains the record of the non-avian dinosaur with most species described, more than 10!
In the 2000s, many new discoveries have furtherly raised its importance, making it perhaps the most scientifically well-known member in the whole dinosaur world. The main discovery has been made in Liaoning, where one specimen has preserved integument which shows porcupine-like quills raising upwards from its tail, for uncertain purpose (Defense? Mating?). These were the very first filamentous skin-structures ever found in an ornithischian dinosaur; this has changed our perception of bird-hipped dinosaurs, which might be more similar to birds than previously thought. Indeed, a few scientists now argue those quills (or similar structures) could also be in all the other more evolved ceratopsians, Triceratops included. Another unexpected discover made in year 2000 in the same site, did debunk the classic “Mesozoic mammals were underdogs ruled by dinos”: the cat-sized carnivorous mammal Repenomamus has been found with baby Psittacosaurus remains in its ribcage!
The "sheep" of the Cretaceous: Leptoceratops
Try to tell everyone if Protoceratops was really sheep-like. If you manage to do it, then try with this: Leptoceratops, the same length of Protoceratops but partially bipedal. Leptoceratops has probably been the most common basal ceratopsid in docu-media after Protoceratops & Psittacosaurus; like the former, it too was compared with a sheep in the past.
The first small-sized ceratopsian discovered (1910s), it was more primitive than Protoceratops, being not only hornless but also bumpless, much slimmer-bodied, longer-legged, and with a much smaller frill. There is a surprising thing at this point: contrary to what one might expect, Leptoceratops lived later than Protoceratops, at the very end of the Cretaceous. And roamed North-America, not Asia (where ceratopsians started their evolution), thus sharing the lands with Triceratops. But for some reason, it had preserved the archaic bodyplan of its primitive ancestors.
Another relative which lived along Leptoceratops is the quadrupedal Montanoceratops, from Montana; once thought to have had a small nasal horn we now know it hadn't such a thing. Protoceratops, Leptoceratops and other animals made once one family, the Protoceratopsids; now Leptoceratops and Montanoceratops make their own family, Leptoceratopsids. Another former protoceratopsid, Asian Bagaceratops, has been recently put in its own family as well. Bagaceratops is notable because is one of the smallest quadrupedal dinosaurs that ever lived: only one meter long, only a bit more than the bipedal Microceratus (see below).
A slimmer cousin: Microceratus (once called "Microceratops")
Despite their partial bipedality, Psittacosaurus and Leptoceratops was still robust guys compared with, to say, the “gazelle dinosaur” Hypsilophodon. But they had also some slimmer relatives, which if they have had a normal-looking head, they’re surely be mistaken for ornithopods.
The most historically relevant was aptly called “Microceratops”. From Ancient China like the prototypical Protoceratops, it’s one of the smallest dinosaurs ever, only the size of a rooster; and was a fast-running animal with slim body and agile legs, unlike the classic image of ceratopsians. Nonetheless, its head was unmistakeably ceratopsian, or rather, protoceratopsian. Very poorly-known, “Microceratops” has now fallen in disuse being preoccupied by an insect: we now need to call it Microceratus. Still, the microceratops has appeared in some popular works, namely the first Jurassic Park novel and Disney's Dinosaur.
The missing link: Zuniceratops
Differences between Proto-ceratopsids and Real-ceratopsids are considerable. There should have been at least one intermediate form between the two: how could it have looked? In 1998, the answer was found under the name Zuniceratops (which has detained the record of “the last member of the Dinosaur Alphabet” for some years). The most ancient North American ceratopsian (Middle Cretaceous), it was only 4 m long and had a mixed Triceratops / Protoceratops appearance: two long frontal horns like the former, and none on the nose like the latter.
This Mix-and-Match Critter look surprised scientists, which used to think frontal horns were a very evolved trait of some advanced ceratopsids - while the nasal one was believed the most ancient horn in ceratopsid’s history. The ancestry of the frontal horns was confirmed in the 2000s, when some early centrosaurine true ceratopsids (the no-frontal-horns subfamily) showed long frontal horns like those of a chasmosaurine: Albertaceratops is one example. Now scientists think later centrosaurines (Centrosaurus, Styracosaurus and so on) reduced secondarily the length of these horns. There was also a chasmosaurine which eliminated its nasal horn, resembling a Zuniceratops; this one is variably classified either as a odd-looking Triceratops species, or a separate genus, Nedoceratops, originally called "Diceratops" ("two-horned face") or "Diceratus" (the name "Diceratops" was pre-occupied by an insect and had the same fate of "Microceratops").
The other missing link: Yinlong
Another, even more important missing-link was found as recently as the 2006: following the current trend about Chinese dinos’ naming, it was called Yinlong. Living in Late Jurassic, it now detains “the most primitive ceratopsian” record. Its external appearence was the least Triceratops-like one can imagine. Yinlong had neither any parrot-bill, nor spiky cheeks: its only ceratopsian trait is a merely anatomical one, the “rostral bone” at the tip of its upper jaw, present in all ceratopsians and in no other dinosaur group. To compensate, Yinlong had small “canines”: this, together with its tiny size and shape, makes it quite similar to the basal ornithischian Heterodontosaurus. Indeed, this resemblance was once cited as the definitive proof that heterodontosaurids were not ornithopods but ancient relatives of ceratopsians and pachycephalosaurs, but now the latter is disputed.
Many new basal ceratopsians have been described since the 1990s both in Asia and in North America. Some were related with the examples listed above: for example, Udanoceratops (one of the largest ones) was close to Leptoceratops; Graciliceratops was similar to Microceratus; while Turanoceratops was perhaps close to Zuniceratops and maybe one of the ceratopsids' ancestors. But others have revealed to be more primitive, if not at the same degree of Yinlong. Two of them have become the namesakes of their own family: the Early Cretaceous Archaeoceratops ("ancient horned face") was a sort of middle-way between Psittacosaurus and Leptoceratops; and the Late Jurassic Chaoyangsaurus (originally called "Chaoyoungosaurus" or "Chaoyangosaurus" and initially believed the earliest pachycephalosaurian) has been revealed being between Psittacosaurus and Yinlong. Still mysterious is the identity of the poorly-known Early Cretaceous Stenopelix, whose pelvis was found in Europe in the XIX century.