Well, I'm glad you asked! A "Chelonian" is a reptile belonging to the Order "Testudines". In other words, "Chelonian" is the scientific name for turtles. Except it isn't... It is an outdated scientific name for turtles that used to be used when the Order was called "Chelonia". It is no longer called that, so, technically, the real scientific name of turtles is "Testudine". But I chose to use Chelonian for this site because I think it is much easier to type out over and over! Although, what does it even matter? Turtles have one of the most confusing (and controversial) taxonomy of any animal, so anything is likely to change...
A reptile is a little hard to define because of their weird taxonomy, but I will give you some basic traits to help you identify them (their synapomorphies if you are a weirdo...). A reptile is usually ecto-thermic (cold-blooded), this means that their body temperature is the same as the environment they are in. Humans, on the other hand, are endo-thermic (warm-blooded), which means that we produce our own heat. Reptiles usually have "plates" all around their body. These plates are called scales... Except for when they are not. For example, a turtle has scales, but the scales on its shell, specifically, are called scutes. Easy, right? All reptiles are vertebrates, meaning they have a backbone (the equivalent of a human spine). All reptiles lay eggs... except for those that don't. Yeah, some reptiles, like some certain species of Boa Constrictors, give live birth. Now, if you want to get into the nitty-gritty of what makes up a reptile, I will happily oblige. Reptiles are charaterized by their lack of (or very reduced) tabular bones. These are bones that protrude out of the back of the skull and are not found in any reptiles. Now, to get even more scientific. Technically, there are two clades of reptiles: Eureptilia and Parareptilia. Parareptilia is what you would usually think of dinosaurs as. They are the older, usually extinct, reptiles. Eureptilia is what you think of as "normal" reptiles: snakes, crocodilians, turtles, lizards, and tuatara (and birds...). Alright, stay with me, this is about to get really nerdy. So, to distinguish between Eureptilia and Parareptilia, scientists look for holes in the back of the skull (called temporal fenestra). A member from Eureptilia will have holes there (meaning they are a diapsid), while a member of Parareptilia will not have any holes (meaning they are an anapsid). However, it isn't that easy, some Parareptilians have temporal fenestra, and some Eureptilians lack temporal fenestra.To make it even more confusing, some reptiles have a synapsid skull (where they have 2 temporal openings in the skull)! (Also, technically some diapsids with a synapsid skull are called neodiapsids... I hope that isn't confusing.) This happens in both clades! This characterization is so weird and fluent that scientists still argue over whether or not turtles are Eureptilians or Parareptilians! So, there you go... A very easy to understand (not) description of what a reptile is!
If you don't know what a turtle is... Never mind. I'm just going to judge you silently... And also tell you (because I'm nice)! A turtle is a reptile (usually belonging to the Order "Testudines", but sometimes not) that has the iconic characteristic of a shell. In extremely simplified terms, a turtle's ribs and spine expanded and fused together to make a bony covering over their body, which some of them can hide in for defense. Some turtles, like Sea Turtles, can't hide in their shells, but they still use it for defense. Technically, if you wanted to trace the ancestry all the way back to the Eunotosaurus (the, as of now, recognized ancestor of all turtles), all turtles (and turtle ancestors, known as stem-turtles) can be found within the Pantestudines clade. Even more technically, all turtles (and stem-turtles) with complete shells are in the Testudinata clade. Also, the Eunotosaurus is in the Pantestudine clade, but not as the common ancestor... That's not confusing at all... Anyways, we will start with the Pantestudine clade to make the stem-turtle activists happy. :)
Let's start this off right: