Minimal - "the least" as an adjective --> minimal amount of people, minimal losses, etc. etc. Minimum - "the least" as a noun --> minimum wage, minimum specifications, etc. etc. Miniature - small scale replica of something Minor - not as important/big --> minor illness, minor fatigue, etc. etc. (also in music: minor scale, minor pentatonic, etc. etc.)

Minor is second when major is first. Minimum is such term, it is noun and minimal is adjective. Miniature is a work of art in the diminished view.

"The differences between them", not among them.