Basic arsenal is more like:
From a pro skills standpoing, the difference between a "petty" and a regular geometry "paring knife is length. They actually share the same geometry; and in culnary French share the same name: couteau office, perhaps best translated as "everyday knife."
Cooks with good skills find the extra length of a longer petty useful in a variety of situations. However, people whose skills aren't quite as strong find the extra length awkward. Most knife nuts like to think of themselves as posessing mad skilz and gravitate towards a longer petty as a parer. The typical Japanese petty is 15cm (6"), and this has become a sort of standard. Also, the couteau office shape is pretty much the same as the slicer. For instance, my "Nogent" petty is marketed as a 6" slicer.
Some paring knives have special geometry for special tasks like the bird's beak, sheep's foot, and so on. But "special task" is really the name of the game with these knives.
You've got a good point about conflating the longer petty with a utility as they're in the same length range. I didn't go to culinary school, instead acquiring my knowledge base of knives and how to use them coming up in a very old fashioned brigade system. The rest of my professional career was either very high end or in my own catering company. In any case, a "utlity" knife was more used for packages and string than food prep. The concept of a utility knife seems a lot more home-cook than professional.
I use my petty almost exclusively for food prep, and something cheaper -- a Forschner Rosewood flexible (wide blade) filleting knife -- for the utility purposes which put a lot of wear and tear on a blade (and for citrus as well).
Anyway the couteau office profile excels at almost everything suited to it's particular length -- except chopping and highly specialized tasks. If you look at our respective lists of the basic blades, neither of us included a boning knife. In fact, a petty is a better shape for almost all boning tasks -- especially "breaking" chicken -- than the normal European desossuer.
Chef's knives/gyutos come in several different flavors of profile. One thing they share which contrasts them to slicers and couteau office, is a high choil -- making for a wide profile at the heel. This allows the cook some very useful knuckle clearance for "push cutting" (i.e., chopping straight down). You can chop with a narrow blade but you either have to mickey mouse the handle of your knife off the board, or really know what you're doing. In either case, it's a chef's profile is easier.
For example (not necessarily a good one, either), I have a 7" "Nogent" chef's knife which I bought specifically for those tasks where I wanted the extra point control which comes from a shorter length, along with the extra blade width that allows chopping without paying too much attention -- in other words, a shallot specialist and sort of deba for small fish. I'm actually quite fond of the knife and find other reasons to use it. But chopping aside, it's not nearly as useful as the petty and it really doesn't do anything I can't do with my 10". It's actually a lot like a santoku in many ways.
Because it's a "special purpose" knife for me, doesn't mean you're not allowed to love it as your go-to.