You usually see this technique on infographics and brochures, and sometimes magazines:
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I don't know if there is a universal term for this. However, I have seen the term slab text used to describe it (not to be confused with slab serif).
I also can't tell you the origin of the technique, however it was very popular during the wood type era...perhaps due to wood type becoming plentiful and more available in a variety of styles and sizes.
(Note the alternate 'A' and 'N' in the 'A NOVELTY' line to 'cheat' the line to full width)
For what it's worth, the example image you provided looks really nice, but I think is a good example of where not to use it: when creating info graphs. It's very much a way to make type more of a visual decoration, which is great for a poster, but isn't really a good way to a readable explanation of complex data. My two cents.
This style is also called justified
The start and end of text lines are both aligned to the left and right.
While justified alignment looks clean because it fits neatly into a box, it can also be hard to read because there is less visual cue between the termination of a text line. Variances in spacing can appear between words in order to keep the lines even.
The size variations in words is called typography. Designers achieve this kind of style using various techniques as kerning, tracking and changing the size of the words.