I have been racking my brains over the differences between laser spectral width and something called the linewidth. The linewidth was written about in detail by Henry in 1982. The spectral width is the width at -20dB down from peak of the wavelength spectrum of the laser. I am looking at some laser data right now that is saying that laser x has 10 kHz linewidth and 60 pm spectral width. You can convert spectral width from frequency to wavelength as in this article and I have done that calculation. By that calculation, a laser with a linewidth of 10kHz should have a wavelength width of about 1x10^-6 nm, not 0.06 nm. Linewidth is often measured with self-heterodyne technique, not a spectrum analyzer. What am I missing?
I assume you are looking at a diode laser (LD) data sheet. In practical terms, spectral width is a measure of tunability of the LD as you vary injection current and temperature. This is quite useful in experiments (say atomic physics with alkali atoms).
The linewidth is related to the phase noise of laser. It is very complicated to derive the linewidth from first principles. Agarwal is a standard reference if you wish to know more.
A practical semi-conductor LD has a typical free running linewidth of 40Mhz. This means, the uncertainty in the frequency is 40MHz. However, this entire frequency band can shift with changes in temperature and fluctuations in injection current.
This rather broad linewidth can be narrowed by optical feedback to obtain the so called external/extended cavity diode laser (ECDL). Check out this seminal paper by Weimann and Hollberg (pdf) for more information. I have built many ECDL systems from the ground up with sub-MHz linewidths. It can be quite a tricky endeavor.
Measuring the linewidth can be quite tricky. The usual direct technique is to beat the unknown laser with a known standard reference and study the beat signal. The equipment necessary is very expensive. However, you can make rough estimates from say a simple saturation spectroscopy based frequency locking setup by studying the amplitude fluctuations of the "error signal". Granted that it is crude and limited to the natural linewidth of your atomic system, but it does not need super expensive equipment or complicated electronics. There are other ways to use atomic physics (EIT, CPT resonances etc) to make reasonable estimates of laser linewidth and it all depends on what your goal is.