fwhm (Full width with half maximum) is the value of pulse width at 50 % of peak value. The value depend upon peak ans well as rise and fall time of a pulse, it turn, depend upon media-material characteristic through which frequency is travelling.
From the image attached to your question (37a.BMP), it seems that you have two signals, at 1320nm and 1338nm, for more details of the signal change the settings on the OSA to start from 1310nm to 1350nm, and change the resolution to at least 0.1nm, even better at the minimum of 0.02nm. You are using a very high value for the resolution, of 2nm, that's why the peaks don't seem to have a shape and you are getting confused, and each signal should have its own FWHM.
Kindly signifies me the importance of resolution for measuring spectrum. Why we are getting less wavelength at lower resolution and more wavelengths at higher resolution?
In a spectrum, when you change the resolution,the 'Q' of detection circuit and Impedence gets changed. This changes Bandwidth of circuit, hence the response
Then which one will be correct as at 2 nm resolution I am getting more oscillating peaks and at 0.02 nm resolution I am getting very less oscillating peaks. I have attched images too.