I remember first installing Gentoo…printed the whole manual and followed along. After a failed attempt and second successful install I learned enough to know that I could use a LiveUSB of my choosing and chroot into the install. Good times!
On Gentoo, it is also simple to install a completely new system in a chroot environment, even if it is intended for a computer with a different, but compatible architecture.
This is frequently very convenient if you want to install Gentoo by compiling everything from sources on a cheap and small computer, e.g. one with some Intel Atom CPU.
Instead of compiling anything on the resource-constrained computer, you install a fresh Gentoo system for it, in a chroot environment on a fast desktop computer, which supports a superset of the ISA of the small computer, so you can still execute the programs intended for the target computer.
Then you just copy the installation result over the SSD/HDD of the destination computer. If you have many identical computers, you can copy the installed Gentoo over all of them without any problems, removing the need for multiple installations.
If desired, you can keep the chroot environment with the installation result and perform any later updates on it. Then you synchronize the updated Gentoo from the chroot with the one or more target computers.
Debootstrap is for installing a minimal system into a dir from another running system (so only useful in the setup phase), whereas arch-chroot is used to access an already installed system (e.g. when booting off a USB stick to fix something). They're not the same thing. The debootstrap-like tool in arch is called pacstrap.
