I often find this kind of table to present a font, showing a sample of characters, the name of the font, a word (random?), and the alphabet. There's a lot of them in the Wikipedia page about the Vox-ATypI classification.
Has it a specific name? Is is standardized somehow? Are there templates available (yes I'm being lazy here)?
All the images seem to come from the same source mostly GearedBull (Jim Hood) user on Wikipedia. It is a type specimen although quite smalll compared to standard specimens. To me, it just looks like someone took the time to make these images for Wikipedia.
I doubt you could easily edit the file since the font is probably in outlines but you can gather some parts by opening the svg in Illustrator. Please take into account the CC license. You can remix but you need to attribute credit and share alike.
Also, see this Typophile post to get more info on what is desirable in a specimen.
There's no specific term other than "type specimen" which is simply some sort of design to show off the design of your typeface.
Historically, back when fonts where physical things made out of wood or lead, you'd receive a catalog from the type foundry with their fonts displayed in the book in various ways, though typically in the form of short sentences or words:
The 'small web image' format is just a variation of that, albeit smaller and designed for the screen. It's a style adopted by Wikipedia as well as MyFonts.com
A variation would be a 'glyph chart'. Like a type specimen, it's for showing off the font, but in this case has an additional task of indicating every single glyph contained within the font. The small image is, of course, not ideal for that type of type specimen.
