Is there a particular name for this "picture of a baby seal in the comments section of facebook" of this image? I know there is "photo comment" but it doesn't point out that it is a cropped picture from the original.
You can use the word snippet.
The cropped image is a snippet of the original. (Although primarily used when referring to an extract of textual information, the word is very much applicable).
In fine art, a very small section of a larger work such as this might be called a detail. OED has
a. A minute or subordinate part of a building, sculpture, or painting, as distinct from the larger portions or the general conception.
but beyond that I can find little in the way of explicit definitions. Searches such as "a detail from the sistine chapel" or "a detail from the fighting temeraire" return plenty of usage examples, though.
It's known as a Thumbnail
Thumbnails are reduced-size versions of pictures, used to help in recognizing and organizing them, serving the same role for images as a normal text index does for words. In the age of digital images, visual search engines and image-organizing programs normally use thumbnails, as do most modern operating systems or desktop environments, such as Microsoft Windows, Mac OS X, KDE (Linux) and GNOME (Linux).
When displayed on its own, a piece of a larger visual work of art is often called a detail.
n. A discrete part or portion of a work, such as a painting, building, or decorative object, especially when considered in isolation.
Definition courtesy of wordnik.com
You've already got the term. It's a cropped image.
Example from wikipedia page Cropping (image). Note that each example is labeled as simply "cropped image".
You can simply refer to it as an edit.
to expunge; eliminate (often followed by out)
The cropped picture is an edit made from the original picture.
Zoom. Lots of valid answers here but I'd call it a "zoom". The precedent, particularly in popular Web usage and where the cropped image appears in proximity to the original is not uncommonly used as a kind of reaction GIF or more specifically a "zoom meme".