This is the best way to describe it found on Adobe forums (again, I'm not yet happy owner of Affinity, waiting for Indesign alternative to buy all 3 programs): Converting changes the pixels’ RGB-values to maintain the color impression while assigning leaves the numeric values unchanged but uses a different profile which can cause the appearance to change significantly.
Like in PS you can press ctrl+Y on rgb document to "see it in cmyk", but for more complex files there will be difference between this and converting it to CMYK (and it depends on actual profile you'll use). and if you are changing between rgb-rgb profiles (or cmyk-cmyk), you can assign profile OR convert it.
ps, if you are not working on image for later hq print (mainly web image and/or something that has to be as similar as it get everywhere, like logo), use sRGB because it has way smaller color spectrum than adobeRGB etc. and it can/will be displayed on every screen (only specific monitors created for graphic designers/ dtp specialists can display Adobe RGB, not to mention prophoto rgb, that has wider color spectrum than you can see).
Google "cmyk rgb gamuts", there is no 100% coverage in cmyk and rgb gamuts, in either way. You can have bright red color in RGB, but can't print that bright color in CMYK, but you can have dark yellow/greenish in CMYK, but can't display such color on your monitor in RGB. Plus never assign profiles, always convert your files to profiles.
In general, when I'm designing logo or something important like that, I'm trying to use colors that will display in similar way on screen as when I'm printing them. I don't own Affinity (yet :D) but PS have small boxes next to color wheel, those boxes will show colors you are choosing, sometimes with exclamation mark sign, this indicates you won't be able to print this color (not in CMYK gamut). I'm sure Affinity have same basic functionality, so use that.
As for clients who can't understand the fact that monitors use different "colors" than print and are stubborn about it I have simple solution: Once I did designed some random graphic with specific colors. I chose those colors to show that not only printed colors will be different on professional and home printer, but also they will be different on different screens! Usually explaining the fact that every screen have differend spec, different ICC profile, different material will not only enlighten ppl about cmyk/rgb difference, but they will also realize that color will be different in different environment, on different screens etc.
