Does OCR software work on Mac or Linux?
Yes. Read by Zaweba has a version for macOS and Linux, with Tesseract on every system, macOS's own recognition on a Mac, and the screen text grab.

It does, and Read by Zaweba is one option that runs on all three systems. Alongside the Windows app there is a version for macOS and Linux, built with Avalonia. It reads text with Tesseract 5.0.0 on every system, uses macOS's own recognition as a second engine on a Mac, and keeps the screen text grab.
OCR used to mean expensive desktop software or an upload to a website. Plenty of it is still Windows only. If you split your time between a Windows PC at work and a Mac or a Linux laptop at home, it's useful to have the same tool on each, working the same way.
How the Mac and Linux version differs
The engines are the main difference. On Windows, Read pairs Windows' built-in OCR with the bundled Tesseract engine. Windows OCR isn't available elsewhere, so the Mac and Linux version uses Tesseract 5.0.0 on every system, and on a Mac adds the recognition that macOS itself provides as a second engine.
Tesseract is the one that does layout analysis and gives a confidence for each word, which is what drives the amber shading of uncertain words in the review. So the core of reading a page, checking it and fixing it is the same wherever you run it.
The screen text grab comes along too. Drag round text on screen, from a video, a locked document or a program that won't let you select, and the text is copied.
Getting it
The Mac and Linux version comes as a .dmg or .zip for macOS, and as an .AppImage, a .deb package or a .tar.gz for Linux. The AppImage runs on most distributions without installing anything; the .deb suits Debian, Ubuntu and their relatives; the .tar.gz is there for everything else.
As with the Windows app, Read by Zaweba is free software under its licence, with no account to make.
What the reading is like
Tesseract does the work on every system, so the results on clean print are in line with what Read's tests found on Windows, where Tesseract measured 99.53 percent word accuracy on a clean A4 letter at 300 DPI. Clean, reasonably sized print reads well. Handwriting, low resolution pictures and decorative fonts are unreliable whichever system you use, and Read says so on its Help tab rather than overselling.
Keeping it private
All of the reading happens on your own machine, the same as on Windows. Documents aren't sent anywhere to be read, which matters for bank letters, medical papers and anything else you'd rather not upload. Language packs are the exception, and only when you choose to download one.
Moving between systems
If you work across machines, the point is that you don't have to learn a different tool on each. Read by Zaweba is described as the same app on all three, so the habits carry over: open the page, let Read read it, check the words it's unsure of, then copy or save. On a Mac or a Linux laptop that means you're not left uploading pages to a website just because you're away from your Windows PC.