On my symbols page, some artboards have a pink icon, while some have a grey icon.
What does the pink icon represent? I have searched but can’t find the answer.
Purple is used throughout Sketch to identify components of all kinds — Symbols, Layer Styles, Text Styles, and Color Variables.
In this case, it identifies that as being a Symbol Source, not a regular Artboard. Its label on the canvas will be purple, too. You can learn more about Symbols, including how to turn a Symbol Source back into a regular Artboard, in our Documentation: How to create a Symbol · Sketch
What is the differences between a Symbol and an pink Artboard (pretending?) to be a Symbol? And in what cases would I want to use one over the other?
When I right click on the pink artboard I get an option ‘Convert Symbol to Artboard’
It’s a little confusing.
Thanks!
…and is there a way to convert these artboard-symbols into proper symbols, ideally without needing to break the link to all their instances elsewhere in the file?
The reason is I have the ‘Symbol Organiser’ plugin which is refusing to run because there are artboards also on the Symbols page.
The purple artboard is a Symbol Source — in other words, the source for a specific Symbol. When you first create a Symbol, you’re defining its Source (which is often placed in the “Symbols” page by convention), and creating an instance of it, which is what you use in your designs.
The lesson “Creating and editing symbols” from our Sketch 102 course is a good overview of the basics of Symbols.
I’m not sure I understand your question, @Meza. Namely, what do you mean by “artboard-symbols” and “proper symbols”?
Hi Meza. 
I put this together which should help to describe the different colors you are seeing for Artboard icons in the Layer List, and also how Symbols show as purple icons there, and the difference between a Source Symbol and a Symbol Instance.
Once you have created a Source Symbol, then you can place as many Instances of that Symbol into your document, using the “Window > Insert” option from your menubar.
On my symbols page, some artboards have a pink icon, while some have a grey icon.
I have the ‘Symbol Organiser’ plugin which is refusing to run because there are artboards also on the Symbols page.
If you have grey Artboard icons on your Symbols Page, then it would seem that you have regular Artboards on this page, as well as Symbol Artboards.
You can move them from the Symbols Page to another page simply by selecting that Artboard icon in the Layer List and dragging it up on to the Page name above that section.
When I right click on the pink artboard I get an option ‘Convert Symbol to Artboard.
This is effectively “breaking apart” the Source Symbol, so that it is no longer a Symbol at all, and is just artwork on a regular Artboard. I wouldn’t recommend doing this, unless this is definitely what you want to do, because doing this will also break apart all the placed Instances of this Symbol in your document too.