Difference of amplitude and frequency modulation of lasers
You are confusing wavelength modulation with frequency modulation.  The FM that you are referring to is the signal frequency, the distance between the peaks of the signal that you are modulating.

There are small effects of wavelength shift that is due to driving level that ultimately limit the power/distance and frequency of transmission as this wavelength shift causes symbol confusion.

Think of wavelength as a color.  You can have a red laser blink fast or slow (FM) or bright and dim (AM) or any combination between and more.  And the same thing can happen for a Blue laser.  In actual fact telecommunication lasers are typically in the Near- Infrared and the wavelength separation is much tighter.  And it's not correct to refer to colors.