Most distressed text faces tend to be based on much earlier styles. For something based on text type contemporary with the examples you show, you might look at Coldstyle:
http://www.myfonts.com/fonts/ephemera/coldstyle/

At myfonts.com…

Decimosexto NF (plus Italic)
Igvaoeonic Oldestype NF
John Alden NF
Maple Leaf Rag NF
McKenna Handletter NF
Ragged Write NF (plus Italic)

That "distressed" quality is an artifact of the scanning, not the printing. You are largely seeing the pixelation resulting from the low resolution of the scans. You could easily replicate this by choosing any font you like, printing something in it, photocopying it a few times (copy the copy repeatedly), and the scan it at a low resolution. You can probably also fake it in Photoshop etc.

The difference between the pages of the Jstor article is that the first page is a PDF generated directly in software with vector-based fonts, and the second is a PDF of a raster image scanned from paper. Make sense?

You can do all kinds of effects on rendered text (with Photoshop) but if you want a certain style of font to come out a certain distressed way directly you'll need a font designed like that. Just asking: is it possible you might have a budget to have such a custom font made? If so there are a number of regulars here who can do it for you, including yours truly: hpapazian at gmail dot com

hhp

There are free font editors where you can import scan-and-traced letters and form a font. Just know: it's not easy getting acceptable results.

Hopefully you can find a font that comes close enough to what you need.

hhp