The laser emission is due to the (excitation and subsequent) relaxation of a quantum system (atom, molecule, ion, etc.)
If the fluctuation in the frequency/wavelength is due to a phenomenon that is the same for each quantum emitter, there is homogeneous broadening, while if each quantum emitter has a different type of fluctuation, the broadening is inhomogeneous.
In these cases each system is affected "on average" in the same way (e.g. by the collisions due to the pressure).
The most frequent situation in solid state systems where the fluctuation is different for each system (inhomogeneous broadening) is when because of the presence of dopants, the local electric field is different for each emitter, and so the Stark effect changes the energy levels in an inhomogeneous way.
The homogeneous broadened emission line will have a Lorentzian profile (i.e. will be best fitted by a Lorentzian function), while the inhomogeneously broadened emission will have a Gaussian profile.
One or more phenomena may be present at the same time, but if one has a wider fluctuation, it will be the one responsible for the character of the broadening.
These effects are not limited to laser systems, or even to optical spectroscopy.
They are relevant in magnetic resonance as well, where the frequency range is in the radiofrequency region for NMR, and one can also refer to these effects in EPR where the lineshape is observed at fixed (microwave) frequency and in a magnetic field range.