Short answer
A colour space is an agreed way of turning a colour into numbers. Different spaces exist because they are built for different jobs — driving a display, mixing ink, or matching how people actually perceive differences — and a set of numbers is meaningless without knowing which space it belongs to.
RGB describes a colour by how much red, green and blue light to emit, which maps directly onto how a display works but corresponds poorly to how colour is experienced: equal numeric steps do not look like equal changes. HSL and HSV rearrange the same RGB information into hue, saturation and lightness or value, which is far easier to reason about when adjusting a colour deliberately. They are still tied to the underlying device, so the same RGB triple can look different on two screens.
CMYK describes how much cyan, magenta, yellow and black ink to lay down. It is subtractive — ink removes light rather than adding it — so it is not a rearrangement of RGB but a different physical process. Converting between them always involves compromise, because each can reach colours the other cannot. A vivid screen green frequently has no CMYK equivalent, which is why printed material can look flatter than the design did.
CMYK values are also press- and paper-dependent, so a conversion without a specified profile is an approximation rather than an answer.
CIELAB was designed so that numeric distance corresponds roughly to perceived difference, with a lightness axis and two opponent axes. LCH presents the same information as lightness, chroma and hue angle, which is usually more intuitive. OKLab and OKLCH are more recent designs that improve on CIELAB's known weaknesses, particularly around blues and in producing gradients that look even. These are the spaces to reach for when the question is 'how different do these look?' rather than 'how do I display this?'.
A gamut is the range of colours a given device or space can represent. No device covers all of human vision, so colours outside a gamut must be mapped to something inside it, which is where reproduction differences come from. ΔE is a measure of perceived difference between two colours in a perceptual space: values around 1 are near the threshold of noticeability for adjacent patches, and larger values correspond to increasingly obvious differences. It is the number behind any honest claim about how similar two colours are.
Wavelength ranges and perceptual thresholds are given as approximations: both vary between individuals and with viewing conditions, and sources differ on exact boundaries. Where a figure is contested or unavailable, this page says so rather than picking one.