During the installation process I can check the box 'Install third-party software for graphics and Wi-Fi hardware and additional media formats. [...] Some is proprietary.' I think there might be some drivers then that are proprietary. Also, if I install apps manually there might be some that are not open-source. However, which other parts of Ubuntu 20.04 are proprietary by default?
The kernel of common linux distributions quite inevitably contain some proprietary binary "blobs" in the kernel for hardware drivers. Without such blobs, hardware support of linux would be much more seriously limited that it is already to some extent.
Apart from that, the presence of proprietary software in most linux distributions is quite limited. Ubuntu does not install proprietary applications by default. However, it offers proprietary software through the Software center or Snap store, and it can offer to install additional proprietary drivers for graphics cards or modems. So you need to inform yourself about the software license before installing additional software if this is a concern.
Ubuntu packages are classified into four components based on two properties: a “fully supported” core vs other packages provided “as is”; free vs proprietary software. “Main” is fully supported and free, “restricted” is fully supported and proprietary, “universe” is as is and free, and “multiverse” is as is and proprietary. By default, Ubuntu only enables packages from the “main” component. If you tick this checkbox, the “restricted” component is enabled as well. You can enable “universe” and “multiverse” after the installation. You're asked about “restricted” during the installation because your hardware might require proprietary drivers without which the installation wouldn't work.
Here are a few ways to find the list of packages in a component.
On the Ubuntu website, there's a list of packages per release and section, e.g. 20.04 administration utilities. The component is in brackets if it isn't “main”, so you can search for e.g.
You can also read the full package list (e.g. 20.04), again with the component in brackets if it isn't “main”. There's also a package list with more information including package descriptions (that's actually the list that the package manager uses to know what packages are available, their dependencies, etc.), and this one is sorted by component, e.g. 20.04 restricted for 64-bit PC.
Not all of these packages are installed by default, of course. I can't find a convenient list of packages installed by default. The manifest (e.g. for 20.04 desktop) lists much more than what's installed by default, but doesn't appear to include restricted software. I think what ends up being installed depends on your hardware anyway.
On your own Ubuntu machine, if you've enabled a component, you can read the package list at e.g.
/var/lib/apt/lists/archive.ubuntu.com_ubuntu_dists_focal_restricted_binary-amd64_Packages (adapt for your download mirror site, version, component and processor architecture). With aptitude, you can list installed packages from a component with e.g.
aptitude search '~srestricted ~i'
To list available packages and not just installed ones, remove
The kernel Ubuntu is built upon will have firmware blobs. Those are required for hardware t work.
However, which other parts of Ubuntu 20.04 are proprietary by default?
None as Canonical does not "pay" for software to be included in the default. That kind of software would have to be included in a different repository than "main".
All of the proprietary options during the installation of Ubuntu you need to confirm yourself and are additional. On the install disk there are, since 20.04, firmware blobs for the nVidia drivers but those are not installed by default as you mentioned yourself. Plus those are proprietary for another reason than to make money: those are actually to prevent people from copying code.
To expand a little bit: any software on the installer that is proprietary Canonical needs to pay for. Either a license fee OR a legal agreement limiting usage in exchange for not getting sues. The nVidia blob is on the installer because nVidia agreed to not sueing Linux (in general). The same goes for all the blobs in the kernel.
If any proprietary software is installed by default and there is no license paid or no agreement about it Canonical would be sued. .