Question: What is the difference between a radical and a component (or primitive)?
Answer: First of all it's a question about how they are used. The radical listing - Wikipedia: List of Kangxi Radicals - was basically "invented" as an indexing system making it possible to find individual characters in a dictionary. They can thus also be called classifiers, used as headings in dictionaries.
A component is either the smallest unit - "atom" - in a character or more than one unit "bundled" under one label/keyword. The character for sun/day is an indivisible unit/component for all learning purposes here, but when you for the sake of memorization combines 日 + 一 you get a new label: 旦 sunrise (Heisig: nightbreak). This is then a component used in other characters.
Question: Why at all bother with "Radicals" here and not stick with, say, components or primitives?
Answer: It's the most common term for character components and are used a lot in China, Japan and other countries where Hanzi/Kanji make up the basis of the writing system. Eventually there will be a time when we need to find a character/word in a dictionary using the radicals.
Radical/Component 001: one (yī)
In the beginning there was ONE. As a radical 一 has that meaning of "one" in 三 only, as far as I know: 一 + 二 (radical 7) = 三.
As a component it has several functions and meanings. First of all it's a horizontal 'delimiter': horizon, floor, heaven, ceiling etc. It's very common to have things hanging down from 一 or reaching up to the roof/ceiling/top:
不 天 下 干平 雨
The other way around it can symbolize the ground/floor/horizon/bottom in the characters
上 旦 丘
So what's the purpose of turning "one" into other meanings? Memory! Not all of us have perfect visual recall or a memory able to store very abstract concepts. It's simply easier to memorize a story than strokes or abstract concepts/symbols. To take a very simple example here (a character you probably will remember as a visual):
"The wizard keeps his magic wand hanging down from the ceiling" or "The fortune teller has his divining rod/staff hanging down from the ceiling". (卜 [bǔ] = fortune telling 下 [xià] = under/down).
Questions/comments are appreciated.