What is the difference between luma and luminance?
There are actually three related terms:


Luminance is a physical measure which represents the luminous intensity per unit area of light travelling in some direction. The units are candela per square metre. This is, if you like, an objective measure of how "intense" light is.
Relative luminance is a measure how "intense" light appears to a human; since humans can't see X-rays or infra-red, that doesn't register. The CIE standard defines a "standard observer" (more on this later) under various conditions. This is normalised into a range from 0 to 1 or 0 to 100, where the higher value is a reference white.
Luma is defined as the relative luminance calculation performed on a gamma-compressed video signal.


So if you take a real-world light source, and point an image sensor at it, the image sensor will output $R'G'B'$ values, where the prime denotes gamma compression.

If you were to uncompress those signals (i.e. convert the gamma-compressed $R'$ into its corresponding linear-space $R$, then:


$Y = 0.2126 R + 0.7152 G + 0.0722 B$ is the relative luminance
$Y' = 0.2126 R' + 0.7152 G' + 0.0722 B'$ is the luma


Relative luminance is exactly Y in CIE-XYZ. Y is calculated by calculating the inner product of the power spectral density of a light source with the luminosity function which represents the "standard observer".

(Note that CIE standard actually defines more than one luminosity function, because the human eye behaves differently in low-light condition; Y is defined in terms of the photopic luminosity function.)

The only reason why we define luma is for signal processing and compression reasons. It's easier to compress based on the luma signal than the relative luminance because the transformation is simpler; in fact, it's achievable using relatively cheap 1960s-era analog electronics. And since there's a more-or-less monotonic relationship between the two, luma key is close enough to keying on relative luminance.

OK, now to your questions:

When I have my images, are the pixel values already in linear RGB components or are they gamma corrected RGB components? That is, how is luma represented internally in imaging systems?

High-quality image formats tell you. Along with an array of triplets of numbers (which are just numbers), there should be information about what colour space the image is in.

Unless you have been told otherwise, it's safe to assume that any standard dynamic range still image pulled off the Internet is in sRGB. This is gamma-compressed, although the gamma is not constant.

For video, there are lots of colour spaces in use. Broadcast television follows the ITU-R recommendations (e.g. Rec 601 is standard definition, Rec 709 is high-definition, etc), and film tends to use Cineon.

But each camera manufacturer typically defines its own colour space too, which represents the best approximation of the sensors in the camera. ARRI cameras, for example, output their own colour space known as ARRI Log C.

It's something of a mess.

When we want to emit the colour in the screen, we perform gamma expansion, is this right? If so, will the light that comes out of the screen be considered as luminance?

"Gamma" is a confusing concept because it refers to two distinct things. Strictly speaking, "gamma" should refer to the nonlinearity of a hardware device, such as a sensor or display. All image data should be linear, intermediate work should be in a linear space, and gamma should only be applied when data is acquired or displayed.

"Gamma compression" refers to a technique for compressing linear data in a file format, so that fewer bits per sample are required.

It just so happens that a lot of modern display vendors and file format designers have agreed on the same standard, sRGB. So if you have data compressed in sRGB format and a display which works in sRGB, the operation of decompressing the file format and the operation of preparing the data for display cancel each other out. In general, that need not be the case.

For a properly calibrated display, yes, Y is relative luminance.

When light waves travel, what physical property does luminance represent? Is it the amplitude of light waves?

Answered above. Luminance is the physical measure of the intensity of light, and relative luminance is the perceived intensity of light (for a standardised human observer).

In the CIE-XYZ colour space, is Y the only one that has physical meaning? Meaning to say X and Z are rather arbitrary factors dependent on the human visual system and nothing to do with physics itself,is this correct?

What I hope you can now see is that Y, relative luminance, is also defined on the human visual system.