Do you genuinely notice differences between fonts? I have a general sense of monospaced vs proportional and serif vs sans-serif. Past that it's mostly all the same to me and I'm kind of impressed that people pay so much attention to the tiny details (and maybe questioning whether they really do or whether fonts are kind of like wine tasting).
I don't think "you" as in "the general user base" notices the differences between fonts, but there certainly is some innate sense of fitness to a design. Similar to how people can tell something is cohesive or jankily designed, even if they can't pinpoint what causes the jank.
Personally, I can't recognize specific fonts in the wild (especially Helvetica and its infinite lookalikes), but can certainly feel when a site uses an inappropriate font (usually too thin, but also things like using a UI font for longer-form text), to the extent I have a few userscripts that change some popular site's fonts to something more appropriate in my optinion.
I just released an update to one of my apps that adds a typography library. Like you said font's are a very subtle thing and as I was converting my app I didn't notice that much. But after pushing the update and seeing the two versions (before and after the upgrade) side by side you see that proper typography can help make an app or a website look that much more "professional". The app before didn't look bad, but it had a sheen of "some guy built this in his basement". Now when I look at the app I get a "ok well a cash strapped startup built this"
I absolutely do. I'm not sure why, it's not something I specifically pay attention to, but I definitely appreciate text in some fonts more than others. For example, I really liked The Economist's print font (and I don't mind the redesign [1])
That said, I once spent a couple weeks trying out various programming fonts/sizes, so maybe I'm an outlier. (I'm on Mac now, and the system Monaco font is fine. I don't remember what I had settled on when I was using Linux until 6 years ago)
I have to add that I recently upgraded from a 2k 27" monitor to a 4k one, and the first thing I noticed is how much nicer all the text is (again, macOS)
That said, programming fonts are a particular niche of interest, because first you want your ambiguous glyphs to be easily distinguishable. O vs 0 vs o, l vs I vs 1 vs i, and secondly you want the overall feel to be pleasing to you.
Other considerations are how does the font render g (is there a loop at the bottom, or just a tail) or a (does it have a "tail" at the top or is more like an o with an extra leg?).
People can get really worked up about these details, just like a coding style guide: if it differs from what you're expecting, it's distracting, but you get used to it after a few days/weeks.
Since last I went on this journey, I see that this wonderful website for comparing programming fonts popped up:
They do. As fast as I can look at a picture of a cat or a dog and tell you which of those animals it is, when my husband sees a font he immediatly knows which font it is. I find it fascinating.
He is also my go to person when I choose fonts because he always give critiques I would never think of.
There is an awesome useful addon if you like hunting down fonts that you came across the sites that uses them. It is called "WhatFont" for Firefox and Chromium browsers. Click the button and then click the font, it will reveal every detail of that font.
Yes! Fonts make a huge difference in the impression a piece of text will make. Just consider that italics and bold have been necessary features of word processors since pretty much the beginning. For an even more subtle example, Twitter's new font is a very plain sans serif, but people are complaining of headaches from reading it: https://news.ycombinator.com/item?id=28156094
I can only recognize the most common ones: Arial, Helvetica, Times New Roman, Calibri, Ubuntu, Comic Sans, Roboto, Computer Modern.
But more than noticing the differences between them, what's important is noticing when there's something wrong in a composition because of the font.
For example, if you show a UI that uses a serif font to someone, they'll notice there's something wrong with it, but most people probably won't tell you exactly what it is.
I don't recognize fonts by name, but I certainly notice differences between fonts all the time. Too thin, too bold, too much space between characters, too italic, more or less impact, how difficult it is for me to read a passage with a given font.