Resolution, generally.

A laser printer operates by using UV light to make fine pigment powder stick to a drum by static electricity. True to it's name, it used to be done via a laser that scanned the drum by reflecting off a rotating mirror - but nowadays it's just as often a line of tiny UV LEDs. The pigment is than baked onto the paper by a small electric oven.

The pulses of the laser and the pitch of those LEDs is generally way finer than what your run of the mill 3D printer is able to achieve reliably. And definitely finer than any nozzle you could put onto a 3D printer.

Theoretically you could DIY the spinning mirror approach, but it would be difficult to source the optical parts, and calibrating it would be a gigantic pain in the ass. Not to mention that it would likely be significantly more expensive than an off-the-shelf laser printer.
Also, guess what happens if you don't have toner cartridge and print drum as one sealed unit. The printing medium is so fine it gets everywhere, ask anyone who ever tried reloading one of those cartridges.

Square Singer explained the difference with InkJet above.

Modern paper printers are deceptively advanced machines. They'd be pretty impressive if not for the greed of the manufacturers. High-precision parts made just right so that you could print out whatever annoying document your employer wants you to actually sign and bring in physically.

A 3D printer is comparatively slow and generally prints in one colour. As I said, you can make a plotter easily by swapping out the print head for a pen, but then you have a single-colour printer that's significantly slower than modern laser printers, that can be upgraded to have multiple colours with a toolchanger but won't produce anything near the resolution of an inkjet (or even a laser printer, tbh).

For reference, this is how a plotter at work looks like. Similar to bed slingers, ain't it.

I feel like theoretically it maybe could be possible to turn an SLA printer into a paper printer, with resin solidifying on a page? But then how would you keep the rest of the page from being smudged?

What's different? Basically the whole thing.

A 3D printer (talking here about FDM because SLA really shares nothing at all with a 2D printer) is basically a tiny hot glue gun being moved on three axies by stepper motors. Of course, the temperature and extrusion controls are much more accurate than a hot glue gun, but that's the basic principle. You got a single "printing point" that gets moved around and it only extrudes filament from that single point.

An inkjet printer has one stepper motor that moves the paper and another that moves the print head from left to right. So there too are axies moved on stepper motors. A very simple trait also shared by e.g. CD and disk drives, slot machines, camera lenses and many other things. All these things are as close to a 2D printer as a 3D printer.

The real magic of an inkjet printer is the print head. A print head doesn't have a single nozzle but an array of many nozzles. This way, a printer cannot only print one dot at a time, but instead a few lines at a time. These nozzles are much tinier that the nozzles on a 3D printer, and they also are much more complicated to operate.

A 3D printer just uses a stepper motor to push filament into the printhead, where it melts and is then pushed out of a hole.

On an inkjet printer, you need to either rapidly boil the ink, so that a single vapor bubble appears that pushes just a tiny drop of ink on the paper, or you have a tiny piezoelectric transducer that creats a vibration that then pushes out ink.

This is orders of magnitude more difficult than a 3D printer, and much tinier. You won't be DIYing a working 2D printer from scratch, while that isn't all that hard for a 3D printer. With access to a decent toolshop, you can make all relevant parts of a 3D printer. The same is not true for 2D printers.

To rephrase your question: Why is it that so many people build DIY desktop PCs, but nobody is making a DIY flagship smartphone? What's the difference?

Basically everything.

Pen plotters are also much slower than inkjet printers, can't effectively mix inks for composite colors, and are significantly lower resolution than any other 2D print technology. Pen plotters existed before ink or laser jet, they lost their market share for good reasons.