Gaussian confusion!

The Gaussian function is a function, just like "sin(x)" or "ln(x)". The Gaussian distribution is probability distribution whose density function is the Gaussian function. As for the 'line profile of the spectral line' that appears to be an application I am not familiar with. Are you referring to an actual spectrum of light or the spectrum of a linear operator?

 

I think nordmoon is refering to Gaussian White Noise.
If that's the case, then you can get some more info from Wikipedia.
I am quoting from Wikipedia:
http://en.wikipedia.org/wiki/White_noise
"White noise is a random signal (or process) with a flat power spectral density."
http://en.wikipedia.org/wiki/Gaussian_noise
"Gaussian noise is properly defined as the noise with a Gaussian amplitude distribution.
This says nothing of the correlation of the noise in time or of the spectral density of the noise. Labeling Gaussian noise as 'white' describes the correlation of the noise. It is necessary to use the term "white Gaussian noise" to be correct. Gaussian noise is sometimes misunderstood to be white Gaussian noise, but this is not the case."