The rel attribute is only an indicator for the lightbox script. The hrefattribute always link to the document which sould be opend.
So where goes what. We got two elements. One to show an image and one for linking to another document (an image is also an document!). lets start with the linking element, aka a-tag.
<a href="https://wordpress.stackexchange.com/questions/74246/document-url" rel="relationship between the current document and the linked document">Linktext</a>
Now we have a plain link to a document with a clickable text. But we want an image instead of a text. We have to replace the image with the text inside the a-tag.
<a href="https://wordpress.stackexchange.com/questions/74246/url" rel="description">
<img src="image-url" rel="relationship to the current document" />
</a>
Now we have a clickable image that links to another document.
What about the lightbox?
If we want the image as clickable link to another document, we can not use the lightbox. Because the link can only do one thing: display the image in a lightbox or link to another document.
The lightbox script missuse the rel attribute as indicator if the image should display in a lightbox or not. The a-tag is simply a fallback if the lightbox script isn’t available (e.g. deactivated javascript).