Electronic – Laser diode to remove copper layer from PCB

Fabry-Perot laser diodes are lasers whose mirrors are simply the flat cleaved surfaces at the ends of the laser chip.

Distributed feedback (DFB) laser diodes are lasers that have a grating structure in the cavity that produces multiple reflections throughout the cavity. This leads to narrower linewidths than are produced by FP lasers.

(Image source: Laser Focus World)

Another type you didn't ask about is the Distributed Bragg reflector (DBR) laser. A DBR typically has two separate grating regions, on either side of the gain region. They're usually distinguished from the DFB because the grating doesn't overlap the gain region, although there is some grey area and the terms are not always used consistently.

(Image source: US Patent #6638773)

Where FP, DFB, and DBR types describe how the longitudinal reflections that provide laser feedback are produced, the designation gain-guided describes how the mode is confined in the transverse dimensions. In a gain-guided laser there is no waveguide patterned between the reflective structures (end facets or DBR regions). Instead, we rely on a narrow region where current is injected to maintain the transverse mode.

This works mainly because any transvese modes that don't overlap the injection region will see much lower gain and so won't lase.

Because the document you linked is for a laser light show device, I'll assume you want to use this for a laser light show.

In that case, you probably do not actually want the green laser to have equal power to the red laser. This is because of the luminosity curve, which shows how efficiently the human eye responds to different wavelengths of light:

(Image source: Wikipedia)

This shows the human eye is near peak efficiency for green light (around 550 nm) and only about 20% efficiency for red light (around 650 nm). So for two laser beams to appear equally bright for human viewers, the red beam should actually have about 5x more power.

That said, if you just want the green beam to be brighter for some reason, you may be able to replace the diode as you suggest. You'd need the be sure the supply is able to provide enough current for the new diode, you'd want the new diode to be in the same size package as the old one, you'd want to be sure to adequately heat-sink the new device when you install it, and you'd want to be sure you can align the output beam of the new diode to the optical projection system correctly. All of these things require knowledge that might only be available in the maintenance manual of the projection system, if they're published at all.