We call them Regionalbahnen -- if you want to get an understanding of speed and price, go to https://www.bahn.com/en and click on "Further Options" and select only Regionalbahnen (you'll have to click the "From" or "To" box first). They are quite slow, but more importantly during the last 9 euro ticket they were so overcrowded as to be unusable (.. well, obviously not since there's a reason they were overcrowded, but you get me..).

edit: in the English version the correct thing to tick is "Types of Transport" > "Regional services, other trains", after you click the "Further Options" button.

edit2: w.r.t

> monthly pass to the suburbs upstate where my in-laws live (a 50 min ride)

This is usually covered by S-Bahnen in Germany, and those are usually under the same ticket as the underground. In most places ~it's around 80ish for such a monthly ticket.~ (edit3: this last part about the price is wrong, see below.)