Up front: I am not a system adminstrator and my knowledge of FreeBSD-administration is targeted towards getting the programs I have written running.
I've started out with a single FreeBSD machine. Now I've got four up and running. From the start I've used the ports tree for installations.
I'd love to run something like a centralized build and distribution system. There must be some professional term for such a thing, but I seriously don't know. If I would, I would propably be able to find the right infomation.
And that's the question: how (i.e. which tools and/or processes does it take) can I build and distribute FreeBSD binaries from a centralized system?
You should use something like poudriere or tinderbox to manage your build environments. You should be doing parallel builds; distcc allows you to do simple distributed builds and ccache provides a speed-up by caching results.
Once you get the builds working, you just need to export the generated packages.
Here's a how-to for poudriere: https://github.com/freebsd/poudriere/wiki/pkg_repos