I’m a bit puzzled. CSS tricks has an area for comments, but I noticed that the people who comment, have their own link and profile image. I understand that the author of that site is using WordPress.
Is this being accomplished with WordPress or another API?
WordPress supports Gravatar, which is essentially a globally recognised avatar. It uses your email address to match up to a Gravatar profile. As you, and only you should have that email address, it should match up to a singular Gravatar profile, if you have one.
Gravatar.com (same as here), it uses the e-mail address.