Arch - fully rolling
Debian Unstable - fully rolling
Debian Testing - semi-rolling. It's following Debian Unstable with 10-day delay, unless Stable it's about to be released, then packages are frozen (bug or security fixes only), usually for couple of months.
Debian Testing is not recommended for server or desktop use, because security patches can be delayed by 10-days.
The canonical information about debian is supplied by debian.
The stable version of debian, currently Trixie, is the distro that debian releases. It's described as stable because its software doesn't change, except for security updates and for fixes if they are necessary. Bug fixes have usually been ironed out before it's released, so that keeps it stable. The release is also stable in the sense that it doesn't normally "fall over", or misbehave or crash, which is a result of it having been well tested before release. Debian stable is a curated distribution with "release-like quality assurance." See here:
https://wiki.debian.org/DebianReleases.
Debian testing is a branch or version of debian for testing, and not a release. It's primary function is for testing of software before it can eventually be included in the next debian release. The testing version gets lots of new updated software. Software updates appear as frequently as daily. At some point in the future, the testing branch is frozen, so no more software is added. That happens a while before the approximately two year interval between debian releases. The tested software, and remaining bugs are fixed as much as possible during the freeze, and then when declared good enough, it becomes the new stable release. See here:
https://wiki.debian.org/DebianTesting
Debian unstable is a development version or branch of debian which accepts new software continually, and is also not a release. It's unstable in so far as package content is continually changing. It's also less stable in the sense of possible problems with the software misbehaving since it's all the latest software that debian has accepted from the maintainers. If packages survive life in the unstable branch without overt issues, after a few days, often between 2 and 10, the software is moved to testing, for testing. See here:
https://wiki.debian.org/DebianUnstable
Debian testing generally only receives security updates from the unstable branch, so security is always a later addition for the testing branch as the unstable packages are passed down to testing. Those security elements are however, those provided by the maintainers and developers in the software contributed rather than from the debian security team, the latter concentrating more on the debian stable release.
Neither debian testing or unstable are rolling releases in the sense of a curated rolling release like arch. Arch, with the continual rolling in of new packages, is carefully constructed to be a coherent distribution by the arch maintainers. The curated nature of it is managed by the maintainers who can make any small or large changes to the whole system to present it as a polished distribution at any point in its rolling journey. With debian testing and unstable, packages are uploaded by maintainers as they become available from developers. The packages may be broken, hence need testing and bug fixes. They may be waiting for dependencies. There is little or no sense of the polished integrated whole, rather, these branches of debian are primarily for development.
The question often arises as to the "rolling release" nature of debian testing and unstable, because they can appear to be just like an authentic rolling release like arch because they continually accept new packages as time rolls on. To consider them rolling releases however, obscures the facts and nuances of their actual nature and function in the debian ecosystem.
With debian testing and unstable, it's usually recommended that users have some experience with repairing and rescuing systems because of the nature of those branches and the relative absence of that carefully maintained aspect inherent to authentic rolling releases.
In considering the needs of the OP mentioned in post #1, if debian is chosen, it can be made quite light and economical with resources depending on what the user chooses to install. If it needs to be expanded later, debian has a huge repository available. I can't say more without experience of that sort of server.