Ttyjfyk

I am trying to understand the different terminologies associated with the different CPU versions.

Ubuntu 16.04 uses the term "i386" to refer to their 32-bit version of Ubuntu:

http://old-releases.ubuntu.com/releases/yakkety/ubuntu-16.10-desktop-i386.iso

Does the term "i386" here mean that this version of Ubuntu can work on the Intel 80386 CPU (which was introduced in 1985), or does the term "i386" here just mean that this version of Ubuntu works on the CPUs that are decedents from the Intel 80386 CPU?

The Intel 80386, also known as the i386, or just 386, was a 32-bit microprocessor introduced by Intel in 1985. This is termed x86, IA-32, or the i386-architecture, depending on context.

x86-64 is an extension of the x86 instruction set. It supports vastly larger virtual and physical address spaces than are possible on x86, thereby allowing programmers to conveniently work with much larger data sets... After launching the architecture under the "x86-64" name, AMD renamed it AMD64... x86-64 is still used by many in the industry as a vendor-neutral term, while others, notably Sun Microsystems (now Oracle Corporation) and Microsoft, use x64.

So ubuntu ISO support both the flavours.

What is this Multiarch?

Multiarch lets you install library packages from multiple architectures on the same machine. This is useful in various ways, but the most common is installing both 64 and 32-bit software on the same machine and having dependencies correctly resolved automatically. In general you can have libraries of more than one architecture installed together and applications from one architecture or another installed as alternatives. Note that it does not enable multiple architecture versions of applications to be installed simultaneously.

$ dpkg --print-architecture
Figure-1: This Computer system has 64-bit Kernel Architecture.

Multi-arch support allows you to use 32-bit libraries alongside 64-bit libraries.

$ dpkg --print-foreign-architectures
Figure-2: This Computer system also supports i386 Architecture (i.e. supports 32-bit Libraries too).

You are correct...

i386 line has been introduced in 1985, and it was the first publically available Intel 32 bit chip. 80286 and (little known) 80186 were 16 bit, and 8086 and 8088 were 8 bit.

In this sense when you see i368 in the package names and installation images it means that it requires 32 bit operations, but does not require 64 bit ones. Now although 32 bits were introduced rather fast, 64 bit operations were slowly fazed in. Pentium pro line already had some 64 bit operations, but i am unsure if it could do everything that current 64 bit architecture can do. Therefore you do not see a processor version for 64 bit packages, but they actually state that they are actually 64 bit.

Trivia: Did you know that even today when your machine boots the processor wakes up as an 8 bit machine and then needs to be told by a bios that it can do more?

Ubuntu hasn't changed the i386 term regardless of which x86 cpu it relates to. The reason for this is Debian refers to all x86 (32-bit) as i386, and Ubuntu (downstream) has followed suit. (https://www.debian.org/releases/stable/i386/ch02s01.html.en#idm181)

The last of the x86 ISOs for x86 require a i686 class of cpu, so no they won't boot & run on a 80386, 80486 or older cpu classes.

The 18.10 flavor x86 desktop ISOs (Xubuntu, Lubuntu desktops, plus 19.04 ISO's up until they stopped being produced Dec-2018 for those flavors) however will boot on a pentium 4/pentium M grade single-core 686 class.

Yes, 'descendants of x86 30386' would thus be correct using wording from your question. Even though many ISO's have stopped being produced, I have Lubuntu 19.04 kernel 5 running on a pentium 4 i686, and yes x86/i686 is still supported, but it now has minimal install options, and support is reduced (and may not extend to Ubuntu 20.04 LTS, but 18.04 LTS still works with i686/x86/i386)