It depends on how up-to-date your Pi 3B+ SD card is. Since you asked the question in the OctoPrint forum, I'm going to assume you have some version of OctoPi. Tell us more about your existing configuration and we might be able to give you a better answer.
Since there is a recent new release of OctoPi, my suggestion is to do an OctoPrint backup on your existing 3B+ and install the new OctoPi image on a different SD card, install that card on your 4B and restore the OctoPrint backup.
Another option would be to clone (using rpi-clone) your existing 3B+ SD card and then try that on 4B.
I have a USB SD card reader which I use to write new images on my Windows desktop and also on my RPi to do the cloning.
Yes, I am using Octoprint as from this site a few years ago but I keep it up to date, currently it says Version 1.8.6. I don't have anything else installed on the Pi. The only plugins are bed visualizer, auto login, bl touch, and octolapse.
I have a card reader for my windows pc, I'll see what I can do to clone it, thanks for the idea.
As @PrintedWeezl pointed out, it's more about the version of OctoPi than it is about the version of OctoPrint. On your OctoPrint screen, the version of both OctoPi and OctoPrint are shown at the bottom of the page.
The apt command (actually two commands) that you enter from the SSH command line will update your current version of OctoPi as much as possible but depending on what that version is, may or may not bring it up to a point that it will support the RPi 4B.
OctoPi 1.0.0 was just released and to upgrade to that version will require starting with a new SD image (on either a new SD card or your existing SD card). It sounds like an OctoPrint backup (created through the browser and then downloaded) will be all you need to update to the latest and greatest and will definitely support both the 3B+ and the 4B.
I cloned the sd card and the Pi4 booted up and ran Octoprint, camera and all, without any adjustment at all. Thanks for your comments and support. Now I can give the 3B+ to my friend to use OctoPi for his printer!