Diffs are the same as always; you can pick whatever kind you want and build a trike frame around it. Something with a peerless gearbox is your best bet. Check out pedicab stuff for a few examples, ridingmower and kart diffs can work too.
If you need to use a kit that converts a bike into a trike, you're stuck with a very limited selection of things that (from what I've seen so far) are not actually differentials, they are just a way to stick two wheels on the back of a bike, usually powering only one from the pedal drivetrain...sometimes driving both via a solid axle...neither with a diff.
But converting a bike into a trike will leave you with handling and other characteristics you probably won't like, unless you ride at 5mph on perfectly level paths and not in or near traffic.
I've seen some actual single-rider trikes with diffs; there is a recent thread for one in the UK that looks like a peerless diff. Most pedicabs I've seen the underside of look like they have one.
When you pick a diff with an axle already attached you're also picking the way you attach your wheels, so this determines which wheels (at least the hubs) you have to use. That may also determine your braking method--you may be limited to a rotor mounted on the axle and a caliper on the frame next to it, rather than on each wheel, so you're passing braking forces thru the diff from one side to the other, as well as thru the hub mountings themselves, instead of having all the forces at the wheel hub itself.
You can pick a diff without an axle and then work out your own to match your desired wheel mounting method, or you can build your own axle-ends for an existing one, custom hubs for it, etc.
If you're going to run motor power thru the diff, you need to pick one designed to handle that--the typical trike kit stuff is meant for pedal power and is very cheaply made--not the stuff I'd pick to run it thru. Even some of the oldies like a last-century Schwinn single-sided non-diff kit I used as the base axle for the SB Cruiser trike (and Delta Tripper before that) aren't all that tough--Not long ago I sheared thru the cotter pins on it's input sprocket with my very weak pedal power (that only even transmits torque at all for just a second at startup from a stop as it triggers the hubmotors to start running).
A kart or pedicab diff, even one from a riding mower, is more likely to survive motor power thru it. I'd guess $200-$300 starting prices for them these days (used to be about $125 but stuff has gone up a lot in recent years). If it's cheap it might also be cheap....
Also note that using a diff (or any cross-trikeaxle, etc), if it's under your trike cargo bed (or whatever you put over it), raises the CoG significantly. That in turn limits the speed you can go, because you have to stay below the speed at which a suddenly-required maneuver to avoid someone else's stupidity would cause a loss of control or crash. Sometimes that's a very low speed, depending on the rest of the trike geometry.
If you stick the axle up above the bed (or whatever) so it passes thru the cargo space (etc) then you can lower the trike as far as you want, but the axle/etc takes out a significant space that some usages will require for other things.
If you use the axle under the trike *but* don't put the wheels on it, instead moutning them separately to the frame, and then chain or belt driving them from the ends of the axle, you can lower the trike as much as the thickness of the diff allows--just make sure to put the whole diff in the "shadow" of the wheels, so that as you go up driveways, over speed bumps, etc., the wheels lift the diff stuff over them, too. If it's far enough forward or aft to stick out of the cylindrical space formed between the wheels, it's going to hit things you go over that stick up too high.
I'd sit down and make a list of your end-use requirements including braking and vehicle design, and the terrain and conditions the trike will be used in, then work out the power needed to do those. Then look for a diff that fits those, and has all of the characteristics you need.
If you already have a trike that otherwise meeds your needs, you can simply add a diff to it, replacing it's existing axle / structure, adding pillow bearings for the axle as needed if it doesn't already have these for the existing axle.
