Files like .bash_profile, .bash_login, .profile, .zprofile, /etc/profile, /etc/profile.d/whatever.sh all serve the same purpose, the primary aspect of which is to apply things like environment variables at login. Display managers and [login] shells source these things in a predictable precedence order so that environment variables are correctly inherited by children of GUI environment processes and login shells.

Login shells? Well yeah, the point of a login shell is that it invokes login-related tasks like setting environment variables from a profile. That's intentionally separate from the behavior of interactive shells because the environments of interactive shells may have been modified intentionally and shouldn't be "reset" to the values applied at login.

edit: also .inputrc is the readline configuration file for things like shortcut keys in all programs which use readline (not just bash) and .bashrc is for customizations specific to interactive shells

And your explanation what the differences are is for me still circular, exactly like in the man pages: login shell is the one which invokes login-related tasks, and I should care about the difference from the interactive shells. I still have no idea what that even means, it is what exactly happens when?

Anybody knows some sane explanation of these? I admit I never tried to find it, as I tried to read the man pages, didn't find anything reasonable, but knew that it doesn't matter to me. I just want the darn variables to exists whenever I need them. I don't care about the differences. One single place is enough.

But now that you say that you "do understand these mechanisms without evicting too much from" your "brain cache" I'd really like to learn everything about the differences. Specifically, when is one invoked and when another for the user "acqq", let's say, on a default Ubuntu system, and on a default Red Hat system?

Are really more different user shells invoked in different forms for a single user, on a single machine, between the booting of the machine, logging in (in GUI) and then starting a few times the terminal with shell inside? When is invoked and which is invoked when? And why shouldn't be a single place for the variables I want to define? No idea, but I would be grateful to read about it now. Thanks in advance.

PAM uses /etc/environment, and systemd would prefer to have you set up default environment variables in /etc/systemd/system.conf. You can even pass them directly to Linux from your bootloader (unrecognized arguments on the kernel command line in the form foo=bar become environment variables), but the profiles are the generally accepted way of doing it.