Difference between next_post_link & next_posts_link

I’m setting up a template for a very simple blog. I currently have two posts in a category. In the index.php file, when I add the next_posts_link() tag a next button appears at the bottom of the blog and it functions as it should. Fine. When I change it to next_post_link() – because I want the title of the next post to appear as the link – nothing shows up. What gives?

I’ve tried creating a single.php file. No link.
I’ve tried putting the php code before and after The Loop. No link.
I’ve read all of the documentation and scoured the forums. No luck.