In the grinding of coffee, the particle size distribution is the main concern. Finer particles will be more subject to extraction than bigger particles because they have more surface area per volume. Generally speaking, a good grind is a highly concentrated distribution of particle sizes, meaning uniformity of sizes. Total uniformity is not an absolute goal, however, because some diversity of sizes can be useful: having a bit of fines (a nickname for particles much smaller than the bulk of the distribution, usually smaller than $100 \mu m$ and consisting of mostly of bean skin, i.e. cellulose) is commonly celebrated to add a bit of texture and they play a central role in modulating pressure and flow rate of an Espresso extraction process.
Apart from fines and their special role, though, uniformity is key. If there is an uneven distribution of particle sizes, the Coffee Extract will be a mix of under-extracted and over-extracted compounds - and unfortunately, they don’t cancel each other out. It’s just doubly damaging to the taste because some compounds are extracted more easily than others. Flavor compounds will be missing in the under-extracted coffee, while the bitter compounds in the over-extracted side can’t be practically removed.
Each of the Extraction Methods has a different range of ideal grind sizes. For example, Espresso needs fine grounds, Moka medium-fine, Drip Coffee medium, Pour Over medium-coarse, French Press coarse and Cold Brew extra coarse. They differ due to the varying ways (temperature, pressure, duration) in which the ground coffee interacts with the solvent (a.k.a water).
Given an ideal grind size and particle distribution, the problem of grinding coffee is now a matter of execution. How to actually get the ground coffee just right is highly dependent on the design and operation of a good coffee grinder.
Blade grinders are the worst. Its principle is to randomly hit the beans with a blade for a while. You have no control over the output grind size except through timing and intuition. The grind is highly irregular so they’re not very appropriate for most Extraction Methods, except perhaps for long immersions like Cold Brew. A good Specialty Coffee going through irregular grinding might still end up tasting better than the average coffee out there, but it’s a wasted opportunity considering the difference in price between a terrible and a decent grinder isn’t big.
Burr grinders consists of two revolving abrasive surfaces at a set distance form each other. The particles bigger than this gap will be ground down, while smaller particles will mostly wander out of the grinder. This results in a more uniform distribution of particle sizes since the main setting is the distance between the burrs, not the time spent grinding and sheer randomness.
Cheap burrs are usually made of ceramic and they work fine, but metallic burrs cut more cleanly and are said to provide slightly more uniformity. In any case, even hand burr grinders should yield a much better ground coffee than electric blade grinders so this should be the default choice. Even so, not all electric burr grinders are born equal and some might be more targeted to some Extraction Methods (frequently Espresso), depending on their particle size distribution profile and limited configurations.
Flat burrs rely on centrifugal force to push out the particles and requires higher speeds on average. Conical burrs have a lot of cutting surface and rely on gravity to to move the particles outward. Flat burrs are sometimes regarded as the most reliably uniform grinders and therefore prioritize clarity, while conical burrs are sometimes regarded as the type that generates more fines and therefore prioritizes texture. This is why some coffee aficionados defend the idea of preferring canonical burr grinder for Espresso, but the output particle distribution profile of the grinder is highly dependent on the specific design of each model and the burr by itself won’t absolutely define if a grinder is ideal for a particular method.
A variation of flat burrs in which blades are significantly more protruded and grouped, the goal being that bigger particles will get cut (or rather, crushed) if they align just right with the blades (or “teeth”) but otherwise it’s easier for smaller particles to move out of the grinder. Because the teeth are so tall, the base of the blades can’t get too close and therefore the average particle size is pretty big, so they can’t really grind for Espresso. There’s no way to objectively say ghost burrs have any specific advantage, they will just produce a slightly different particle size distribution and this could yield a different flavor profile.
Retention pertains to the capacity of the grinder to actually push out all the ground coffee. A grinder can retain from very little (0.1g) to a lot (2g). This is a bit wasteful but also gets in the way of changing settings like picking a different bean or a different grind size because there will be a bit of previously-ground coffee mixed with the new setting. The retention coffee can also get stale and get in the way of flavor for the next batch depending on how long it sits there.
Cheap electric grinders will compensate the hardness of beans by spinning the burrs faster because this requires a less powerful spinning motor than one that goes slowly but steadily. This usually means these grinders are louder and will have difficulty with finer particles so they might not be capable of providing an espresso-fine grind.
High-end electric grinders sometimes offer adjustable burr rpms. There’s some evidence that higher speeds decreases uniformity and this is specially critical for coarser grinds, though a bit less noticeable on espresso-fine grinds and smaller (Blackwater) In general, higher speeds are somewhat equivalent to just picking a finer grind setting.
Some grinders are single-shot, meaning you can only input the beans that you mean to grind immediately instead of just letting the the whole lot of beans reside on a hopper on top of the grinder and fall through as you grind them. It may happen that the last beans entering the single-shot grinder jump out a little bit because they don’t have other beans on top of them applying downward pressure. These beans jumping out of the burrs is what is commonly referred as popcorning. Generally, faster spinning burrs cause more popcorning - but this depends a lot on the grinder design.
Popcorning is generally not a big deal, as most builds won’t let many beans jump out of the grinder entirely, just causing the grinding to take a bit longer. These last beans are also traveling through the burrs a little more “lonely”, meaning they have more space and possibly grind less evenly, generating more fines. Overall, the impact is small but plausible. As with most things grinder-related, it’s hard to predict and has to be experimentally stablished for each design.