(Disclaimer: I'm Italian, it's fatiguing for me to write in English and moreover to write in technical jargon. Thus, the following explanation take a few shortcuts to be easier to write and to understand)
I'll start from the bottom; increasing ISO in camera cannot obviously be like increasing the exposure of a file, whatever the algorithm used: increasing the ISO means that you are amplyfing the analogical signal (like raising the volume of your stereo, in a certain sense), increasing the RAW exposure means that you are working on the digital data stored in the file. Although in the end you can get a similar result, they are a totally different approach with totally different drawbacks and advantages.
user2719's answer in the third linked question sums it up pretty well: you have a signal, which means Data + Noise. If you use ISO then you are amplifying it, so you end up with Amplified Data and Amplified Noise. Then you digitalize it, which introduces more noises (in a sense), so now you have Amplified Data + Amplified Noise + Additional Noise.
Working with RAW and the camera native ISO, instead, (faking that you don't amplify the signal) (we are trying to keep things simple, ok?) you begin with Data + Noise. Digitalize it, and you get Data + Noise + Additional Noise. Apply an exposure bias in a software, and you get Amplified Data + Amplified Noise + Amplified Additional Noise.
All of this is generally speaking. For example, another thing to keep in mind is that usually the electronic circuits in the camera have been thought and optimized (well, we hope at least, for what we pay it) to work together, so when you raise the ISO is not just some kind of third party thingy that casually found itself in the camera body.
So, in short:
Is it same as I increase ISO when capturing the photo?
No way: an electronic amplifier before the process of digitalization cannot in any way be the same of taking the color value of a pixel and
multiplying it by a given value.
If they won't be the same, what's the difference or which way is
It's always better to proper expose; after that you can play
miracles with a software in case of errors, but otherwise it's like
driving with eyes closed because there are airbags in the car.
Can you provide me some reference of this?
Well, why not? :-)
Copy paste straight from my chosen RAW developement software. Enjoy:
Utilizing Difference between Exposure Biases of Camera and SILKYPIX®
The exposure bias on cameras slows down shutter speed, opens the aperture and in some cases reduces light with ND filters, thereby changing the amount of light falling on the image sensor.
On the other hand, exposure bias when developing corrects the exposure recorded in RAW data and develops the photograph.
For example, consider performing exposure bias of +1.0EV.
By performing exposure bias of +1.0EV on a camera, the amount of light recorded on the image sensor is doubled.
Performing exposure bias of +1.0EV at the time of development, development processing is performed with the amount of light recorded in RAW data doubled.
As a result, both are the same, but they each have their own advantages and disadvantages.
A drawback of increasing exposure bias when developing is that noise is doubled. Compared to exposure bias on the camera, you may result in a photograph with a bit more noise.
However, there are huge merits to exposure bias when developing. One is that it gives you the ability to control over exposed highlighted portions.
When performing exposure bias on a camera, if the exposure bias is too large, it may not record over exposed highlighted portions. There is no information for portions that go over the image sensors dynamic limit, even in RAW data, and there is nothing to retrieve when developing, even when developing with lowered sensitivity. (*1)
Also, the appropriate amount of exposure bias must be determined and settings on the camera be changed when performing exposure bias on the camera. You can reduce the time and labor when shooting and concentrate more on taking your photograph by performing exposure bias at the time of raw development.
Furthermore, exposure bias on the camera often influences the shutter speed, and you must take care concerning camera shake or the subject moving.
Increasing sensitivity during raw development normally lessens noise if at around +1.0EV. This is considered an effective photographic method for digital photography.
Also when it is difficult to determine an exact exposure under shooting conditions such as backlight or so on, take a picture with a little underexposed value using the exposure bias.
There is a more advanced technique. When it is so dark that you have to use a slower shutter value or a faster lens, one smart way is to try to use a low shutter speed or aperture value to result in an underexposed image.
*1 Depending on the type of camera, developing with a lowered sensitivity of around –0.5 to 1.0EV is possible, and you may be able to save skipped portions, but many cameras cannot save whiteouts with lowered sensitivity at development.
Utilizing Difference between ISO Speed Adjustment of Camera and Exposure Bias of SILKYPIX®
The ISO film speed adjustment on the camera usually changes it at an analog level before digitizing the voltage output from an image sensor.
For example, with the ISO film speed doubled, information is doubled and sampled with an amplifier from the image sensor in the camera.
Light quantity recorded by an image sensor does not change just because the ISO film speed is adjusted. Doubling the ISO film speed halves the light quantity recorded by the image sensor.
There are hardly any differences from performing developments with an increased sensitivity of +1.0.
For example, compare photographing with a camera set at ISO 400 and photographing set at ISO 200 and exposure bias of –1.0EV (one step under). Other photographic conditions such as shutter speed and diaphragm stop are the same.
The amount of light recorded by the image sensor for these two photographic methods is the same. The RAW data photographed at ISO 400 is converted and recorded at double the amount of light.
When developing the RAW data photographed at ISO 200 into a photograph, sensitivity must be raised to +1.0EV. However, photographs developed with increased sensitivity are almost the same as photographs taken with ISO 400.
When comparing these two photographs, the amount of light recorded by the image sensor is the same and both are processed in terms of double the amount of light in the end, and the only difference is whether it was performed in the camera or at the time of development.(*1)
When set and photographed at ISO 400, if highlights are ignored, it is impossible to restore them. However, the possibility of being able to save them by adjusting sensitivity rises if you set and photographed with ISO 200 at an exposure bias of –1.0EV (one step under).
As one application, it becomes possible to confidently take photographs of a dark subject that you have to take by raising the ISO film speed on the camera and working with the shutter speed and diaphragm stop to underexpose on purpose.
*1 The processing of photographs at ISO 400 and doubled in the camera can perform processing to remove noise in the camera at an analog level, which is slightly advantageous for the image quality.
However, the difference is not that great, such that the technique of underexposed photography has merits, such as when there is a possibility that highlights may be skipped.