I’m willing to bet that most bars you’ve been to don’t have “digestif” or “apertif” sections on their drink menus – that is, anyway, if you live in America or more specifically anywhere that is not Europe. This is mostly due to two enveloping things:
1.) technically, many of the alcohols in other sections are more or less formally fitting into one of these categories, and
2.) it is not necessarily a part of our ingrained culture to have a particular drink for particular reasons; that is, apertifs and digestifs both have very medicinal and utilitarian histories (and in Europe are still practiced in derivation of those traditions). We don’t really practice alcohol consumption for utility in the good ‘ol US of A, let alone much drinking tradition on the whole; we tend to drink what we want to, when we want to. Because we’re America.
Apéritif: usually something dry, served before a meal. Think fortified wines and champagnes or sparkling whites. Thought to stimulated the appetite.
Digestif: usually served after a meal to aid in digestion, and served straight. Many of these you know, including: tequila, whisk(e)y, vermouth, brandy, and even Kahlua.
(Not sure I believe Kahlua to help with anything but an added-fun coffee creamer, but it is what it is.)
While I haven’t so intentionally played the apertif game, my first-hand experience with the digestif side equals two thumbs up. I regularly digestif. Straight vermouth, as unappealing as that might sound, works efficient wonders for stomach upset.