What is the difference or relation between a Color Model and a Color Space?

A color model is the mathematical (or computer science) way of describing colors. It is independent from physical devices.

RGB-8 or RGB-16 are color models as well as CYMK or HSL.

A color space is the method of mapping real colors to the color model's discrete values. sRGB and AdobRGB are color spaces that both use RGB as model. But in one the color represneted by, lets say RGB(16,69,201) may be differently displayed in sRGB and AdobeRGB.

Another RGB model is describing each "channel" with a floating point rather than an integer. Both sRGB and AdobeRGB would work nicely with this mode.

Lab is a color space that agrees well with the HSL (or HSV, I am not sure) color model.

The color room is called a room because the total number of colors available inclusive of all shadeds of brightness can be shown best in some 3-dimensional corpus, rooms.

They are often used interchangeably because their separation is rather abstract. Practically you cannot really discuss color spaces without having a specific color model in mind.

Another way to add to Hermann's excellent answer would be that when the term color model is used it is used in it's mathematical form, and when the term color space is used it is usually used in the context of data that has had the color model applied to it and thus inhabits that color space.

There is no accurate term "true color" in the context of color models or color spaces, unless it's spectral data and that's not a color model or space. Since color models contantinate spectral data and attempt to create an ordered system of values, it is a safe statement to say that this ordered system of values is based on a single white point and is in itself a metameric system. So the color is no longer true, in the purest sense of that word.

Color model

A color model uses numbers to represent color. For example: Blue is represented as: rgb(0, 0, 255).

Color space

Next, ask yourself: how blue will this blue color be on your monitor? It all depends on your monitor and the color space. Blue is less saturated in sRGB (color space) when comparing it to Adobe RGB 1998 (color space).

A color space is set of colors that belong to a device or mathematical model. RGB is a color model, but there are more then one color spaces based on RGB: Adobe RGB 1998, Adobe Wide Gamut, sRGB.

Actually, color spaces doesn't have to be RGB-based. Other color spaces are: CIE Lab, YUV, HSL, HSV, HSB.

To explain color space to a 6 years old I could say something like this. You have 44 colored pencils, and you may only use these 44 colored pencils to create an image: