They’re both related to how the RGB values are interpreted in the image, but they’re slightly different in what they do.
Not sure how much you know about colour spaces so I’ll give a bit of background, sorry if this is too much detail!
Essentially you have a working image which has RGB values (r,g,b) which vary from 0 to 1, but the question becomes ‘what is red, green and blue?’ Let’s say I have the value (1,0,0) which should be red, what do we mean by red? This is where the ICC profile comes in, it says how to interpret the values in the image into actual well understood colours. Common colour spaces are sRGB, AdobeRGB and ProPhoto etc.
I’m going to move to terrestrial (normal) photography for a moment rather than Astro. When you take a raw photo with a camera, you get a range of (r,g,b) values but they’re just counts of the photons you received, they’re not tied to a colour space at all and it’s not clear what colours they actually map to. Companies like Adobe have actually done lots of tests with all the mainstream cameras and they have mapped the camera (r,g,b) values into each of the colour spaces (usually ProPhoto by default in Lightroom I think). So when you’re looking at a photo in Lightroom it actually has done a transformation:
camera (r,g,b) -> ProPhoto (r,g,b)
Now back in the astrophotography world, in software like pixinsight, it gets a bit confusing what the colours mean especially when we usually apply lots of curves adjustments and stretches, and no one has done lots of colour tests with the standard astrophotography cameras. So they all ignore this transformation from camera (r,g,b) to colour space (r,g,b) and instead they just assume that the values are already in sRGB, i.e. they just directly take your camera values for instance (1,0,0) and say this is (1,0,0) sRGB. You can confirm this by taking a normal terrestrial photo and opening it in both pixinsight and Lightroom, you’ll see the Lightroom image looks like you would expect and is much closer to what it looked like in person, and the pixinsight image will be very different. This could be a whole new topic, about whether this is the right approach, but I’ll leave that for another day.
This is where the assignICC process comes in, you can change which colour space it will use to interpret the values in your image, but it’s not doing any conversions or anything. If you change to AdobeRGB, then it will now directly take camera (1,0,0) as AdobeRGB (1,0,0). You’ll see the image drastically change when you do this.
The transform ICC process is for moving from one colour space to another while keeping the colours the same (with potentially some clipping if you move from a wide colour space to a smaller one). So let’s say you’re transforming to AdobeRGB and using a default image in pixinsight, then your image will be sRGB and you may have the value (1,0,0) but the same physical colour in adobeRGB might be (0.8,0.1,0). The transformation will apply this conversion and then tag your image with the new colour space, so the final outcome will look the same.
So both processes change to a new colour space, but one of them does not alter the (r,g,b) values and the other adjusts them so the physical colour is the same. Transform ICC is probably what you’re after, you can transform to sRGB and it will still look the same. However if you haven’t changed anything your image will most likely already be in sRGB not ProPhoto using pixinsight.
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