The simplest answer is: "Assign" preserves numbers, "convert" attempts to preserve appearance.
in more detail:
If you have something that is looking wonky colorwise on screen, or printing strangely, the fastest, nondestructive way to see what might be going on is by assigning a different profile and viewing/printing again. Assign says all pixels keep your info, I'm just going to use a different set of instructions to decide what your info means visually.
Converting to a new profile does actually change data, color swatches, images, etc. will have new info created that tries to keep appearances as close as possible, but might have to invent new rgb/cmyk values to keep a semblance of the appearance in the new color space. It is destructive, actual information is changed and perhaps lost in the conversion. Think of it like converting an RGB image to CMYK in photoshop, you've actually changed the file and asked it to take the original 3 channels and convert them to the new 4 channel option. If you go back and forth between these actual conversions you start to degrade/seriously change the image/file.
Now, why there are two is for color management reasons. Convert is the correct way to ready something for print once all things are finalized, making sure the color profile is correct for your final print workflow. If you do need to convert the file to a new destination space, then I'd recommend saving an original, and making a new one with the converted space so you could go back readily if necessary.
Assign let's you tinker and at least visually try to figure out why what you're seeing on your screen is nothing like what you might have been expecting. It is not intended for a print workflow, its for helping you figure out what's what.
There are also some use cases where if something doesn't have a profile you want to first assign the one that looks best on your screen, then convert to the correct output one... Anyway, there are a lot of reasons for having both the assign and the convert options.
When I did a lot more photo editing there were some photoshop threads about this I found helpful that led me to:
Hopefully that is helpful!?