Is it important which version of a rolling release I start from? For example, if I download a version of Arch Linux 6 months older than the latest on the website, and then run update & upgrade, isn't it the same of running the same command on the latest version?
In a perfect and smooth world, you would be able to start with a several years-old version and get the same thing after update as if you had started with the very last version available.
Most of the time, when you upgrade your system, everything will work like a charm. But it only needs a few tricky updates (like the systemd/SysV) among the hundreds to get a real mess. And the chance of having such updates grows with the age of the system you upgrade.
So, maybe starting from a monthly-old system will work fine, but I don't get the point of taking the risk to loose time doing boring stuff to get things work when you just have to download a fresh iso to reduce this risk dramatically.
Arch Linux periodically releases an installer image. The Arch installer, unlike the Debian installer, always installs, or attempts to install, the newest version of Arch, regardless of the "version" of the installer (assuming a somewhat recent installer from the past few years). The Arch installer downloads the newest version of packages from the Arch repos and therefore no matter what version of the installer you use, you will end up with an identical system.
The Debian installer installs a specific version of distro. Upgrading from, for example, old stable to stable, should theoretically give you an identical system, but there could be differences in the default packages installed. There could also be incompatibiities in the upgrade pathway, although the Debian team tries to avoid these issues. Using the Debian installer for stable, but a slightly dated point release, will likely install the core packages from the installer image. Depending on the installer type, it might install all packages from the image or it might install the most recent packages from the stable repositiory. After installing, you can update the packages to the most recent version. This is a much more throughly tested procedure and will like result in a identical system independent of the installer version.