In the Nikon D5600 , there is the usual flash compensation setting where you can set it from -3.0 to +1.0 But there is also a setting called flash control in the menu , where you can set the flash to 1/32, 1/16 ... all the way up to full.

Do both of these achieve the same thing, or is there any difference between these 2 ?

Both flash exposure compensation (FEC) and flash power control do the same thing: adjust the power (really the length) of the flash burst to adjust how much light the flash puts out during the exposure. The main difference is that FEC is relative to the current power setting (usually made by TTL), while M power ratios are absolute on the scale of the flash's full output.

TTL (or through-the-lens flash metering) is where a digital camera sets the power output on the flash automatically by having the camera tell the flash to send out a metering "preburst" of a known power level, meters it, and then adjusts the flash power based on the results. M (full manual) flash, you have to explicitly set the power level as a ratio of its full power. Think of this as being analogous to using automated exposure modes on the camera (where settings are adjusted based on metering) and using relative exposure compensation (EC) and M (full manual) on the camera where whatever you set is what goes and you have to explicitly set the ISO, aperture, and shutter speed to specific settings.

Both types of adjustments (FEC and ratios) are given in stops. A stop is a doubling/halving of the light, and is also called an exposure value (EV). So +1EV is the same as going from, say, 1/8 power to 1/4 power.

FEC uses EV as its unit of adjustment. But M power levels that are partial stops can also use 1/3 EV increments, so EV aren't exclusively used for TTL and FEC. But TTL and FEC never use the power ratio settings.

...For flash compensation, image was brighter as it changed it from -3 to 1. And for flash control also image was brighter as i changed it from 1/32 to FULL.

• -3EV to +1EV, is a four-stop increase in light output.

• 1/32 M power to full (1) M power is a five-stop increase in light output. (1/32 → 1/16 (+1EV) → 1/8 (+2EV) → 1/4 (+3EV) → 1/2 (+4EV) → 1 (+5EV)).

That's why using the manual control was brighter than the FEC control. But you were essentially doing the same thing both times. You just did it one stop more with the ratios. Had you set it to 1/2 power, it would have been the same amount of exposure change. But would only have been identical between the two methods if TTL had set your flash to 1/32 power.

The main advantage to using Manual ratio settings is that you know where you are in the flash's output power range. FEC, you may already be at, say, 1/4 +1/3EV power, and while you can ask for +3EV, the most the flash can give you at that point is +1 2/3 EV.

Because FEC is relative to where TTL set the flash's power, you may not be sure where you are in the range, unless your flash has a TTL-locking feature that can translate the TTL setting to an M power ratio (e.g., the TCM function on a Godox V1).