When I am on
Manual flash, I can go from 1/1 to 1/128 and even with 1/3 stops too.
When I am on TTL mode or Remote mode of the TTL flash I can do "exposure compensation" for that flash and for me I think it ranges from -3 to +3 .
Are these the same, or they are two different things?
When I am on
Yes. :) Both are controls of the flash power, but FEC is relative (and only in TTL mode), while the power ratios are absolute (and only in M mode).
FEC, like exposure compensation, is a relative adjustment from where the auto exposure system in the camera thinks the best exposure level is (i.e., it's relative to a shifting "0" on the scale, based upon metering. And it isn't always ±3EV--depending on where "0" is in the range--if "0", for example, is at 1/1 (full) power, then you've only got -3EV possible, because you can't go any higher. FEC of -1EV, however, could represent any power level on the flash below 1/2--it all depends on how the TTL pre-flash metering went. Just a -1EV exposure compensation could mean any shutter speed or aperture setting one stop below your maximum on the camera body.
The power ratios, however, are absolute. The numbers represent the ratio of full power of the flash and do not change with the metering. Like an explicit shutter speed or f-stop setting, you can get more familiar with what that power level setting "means" in exposure results.
Flash exposure compensation (FEC) shifts the metered exposure value for the flash by the set number of stops.
The power levels of the flash in manual mode are fractions of full output (1/1).
So if the TTL metering determines a flash power level of eg. half full strength (1/2) and you have dialed in a FEC of -1, the resulting flash output is 1/4, -2 would result in 1/8.
This is of course equivalent to performing this metering and calculation manually and setting the flash to the calculated power.
FEC is a bias, while the power setting is an absolute value (well, relative to max. power, of course).