So, basically, when you auto-home, that lets your printer calibrate itself with regard to the position of the print head on the X (left-right), Y (forward-back), and Z (up-down) axes, right? For each axis, it just keeps moving in the negative direction until it hits a switch. (An “endstop”.) When it hits the endstop, it considers that “zero” for that axis.

For the Z axis specifically, you have a couple of different options where you can put that switch. You can put it on the frame of the printer and position it such that when the print head moves down, the bar that the print head is on hits that switch at roughly the right place. That’s a “Z-endstop”. Or, you can put the switch on the print head so that it can be moved not only up and down but left and right and forward and back. That’s a “Z-probe”. (The “CR-Touch” is a specific brand of Z-probe sold by Creality.)

With a “Z-probe” your printer can take Z-axis calibration values not just for the arm that the hot end rides back and forth on, but for multiple different spots on the bed. (Typically in a grid pattern.) So, for instance, it can check the front-right corner of the bed, the front-center, front-left, middle-right, middle-center, middle-left, back-right, back-center, and back-left. Once it’s got values for all those spots, it can do some math to get a good approximation of the “shape” of the bed.

Your bed ought to be close to flat, but typically beds – or at least stock beds; again, I’m not sure about the glass beds – will be subtly parabolic or hyperbolic or something. (Like, shaped like a bowl or a hill or a Pringle chip or some such rather than truly flat.) So if you have a Z-endstop and can’t do calibration at multiple points on the bed, then your printer can only act under the assumption that the bed is flat. If your bed is actually (for instance) bowl-shaped, then the print head will be closer to the bed when the print head is far to the front-right, back-right, front-left, or back-left than it is when the print head is closer to the center. In that case, the best you can do is just kindof manually calibrate your Z-endstop offset until you’ve got the most reasonable compromise between too far from the bed when you’re near the center and too close when you’re near the extremities.

(Sidenote: It’s not 100% true that you can’t get your printer to account for bed curvature if you only have a Z-endstop rather than a Z-probe. From what I’ve heard, there are ways to manually “probe” your bed to get figures for the shape of your bed and then give those figures to your printer’s firmware to get your printer to account for bed curvature that way. But it’s a big pain and may have to be redone a lot. It’s been a while since I’ve looked into that option, but I think it may also have required rebuilding the firmware and stuff. As I said, big pain.)

But with a Z-probe, the “auto-leveling” process, when it probes the bed in a grid, it can build a model of what shape the bed really is. And then as it prints, it can follow the curvature of the bed as the print head is moving in the X and/or Y direction in order to stay a very consistent distance from the bed, rather than getting further or closer to the bed (or perhaps it’s better to say the bed is getting closer and farther from the print head) as the print head passes over “hills” and “valleys”.

When your print head is too far from the bed, it doesn’t adhere well and there’s increased risk of the part coming off the bed mid-print. When your print head is too close to the bed, you run the risk of underextrusion, clogs, and first layer expansion. But with a Z-probe, it’ll be better at making sure you get the best of both worlds, and not just on part of your bed. On all of your bed.

The Ender 3 V2 appears to come with a Z-endstop, not a Z-probe. (Just looking at the image on Creality’s official page.) So if I got an Ender 3 V2, I’d add a CR-Touch immediately. (That said, again, the glass beds may have less issue with bed curvature, so it might not be so worth it with your glass bed. If you’re successfully using most to all of your bed and not having adhesion issues or first-layer expansion, there’s definitely no need to worry about it. But it wasn’t until I got a Z-probe that I understood just how reliable my printer could be and how little first-layer expansion I could expect from it.)

One thing to note. Bed curvature with a Z-endstop won’t matter so much once you’re a few layers in. It’ll cause issues with the first two or three layers, but by the time you’re up to five or so layers, it’s not really an issue any more. Most of the issues I had with bed curvature with a Z-endstop before I got my second printer were that the print failed within the first few layers. Usually by popping off the bed rather than adhering as it should.