I'm no expert but I think maybe there's not a massive difference between PDF, PS and AI.
I see you haven't googled the question. :-) That's a bit like saying "I'm no expert, but maybe there's not a massive difference between a lump of coal and a diamond.... they're both carbon, right? " :-)
PS or PostScript is a programming language designed to produce printed pages on printers. When it is used to make stuff appear on a monitor, that's because the window is running an interpreter that pretends to be a printer.
EPS (encapsulated PostScript) is a limited form of PS.
AI format is a brutally simplified subset of EPS, with the addition of many differences.
PDF is yet a different display programming language that, unlike PS, does not contain program flow commands, but which is unlike AI in that it is closer to PS as a language than what is AI. It's as if the programmer who created EPS got drunk and accidentally deleted all his sources, and then tried to re-create what he or she did, with some memory of how he approached the task but then writing it all from the ground up again. So, sure, lots of resemblance but not the same thing.
The problem with all of these approaches is that they were created to get around hardware limitations that were a big factor 30 years ago but which now are long forgotten. But still, they persist because of the large installed base of Adobestuff. Even Adobe itself has trouble sorting all this out.
As display-generating languages, they have some advantages. But as means to generate reproducible vector data they are absolutely, horrifically terrible compared to more sensible means.
By the way, for those who are puzzled by what I mean by a "programming language for display," consider two different ways of storing data about the exact size, shape, and location of a real estate parcel:
Store the data: Start a file by announcing the coordinate system you are using, using an EPSG code. Now, give a list of each coordinate that defines the boundary of the parcel in order, using the usual GIS conventions for islands and inner holes. Done.
Store a description: This is the old "metes and bounds" approach going back to Roman times. Instead of storing exact coordinates, you store a verbal description, such as... "Start at the rock where the corner of Farmer John's property touches the corner of Farmer Fred's property. Proceed south by southwest until you see the big oak tree exactly to your left. Put a rock there to mark the spot and then turn south and proceed 20 paces. Put a rock there and now turn due east..."
That's a programming language description using commands like stepping 20 paces and using program flow control logic like "until you see the big oak tree..." To find out what the parcel is you have to "execute" the "program" by following the instructions in the description.
The coordinate data is more precise than the descriptive way, because maybe not everybody following the programming steps has the same idea as to which of many oak trees is the "big" oak tree, and maybe not everybody agrees on the exact distance that a "pace" should be. That's why different programs which execute any of these ancient programming languages so often come up with different results.
AI is really guaranteed to work only within Illustrator, and at that only within those Illustrator versions that match the AI version, because it depends upon the peculiar internal assumptions made by AI. It's not a good interchange format and Adobe has never pretended that was the mission for AI. Adobe intended AI only to solve a specific set of issues 30 years ago, in a setting where they had to get Illustrator going to provide vector capability that was totally lacking in Photoshop.
It's a terrible hack that persists in the modern world, like some ancient snippet of virus DNA that's become embedded in the human genome, ready to wreak havoc should cancer or some other mishap throw the "on" switch for that sequence.
As for supporting AI, it would be far more effective in terms of providing ease, a great life, and wonderful capabilities to simply provide those vector editing capabilities in Manifold that Illustrator has, which you need to use. Illustrator is not so good at handling large data, so it's not like you will not have to find an alternative sooner or later.
It's like you have a crew of guys who are building houses for you and one of them, an older guy, is a first rate electrician. He does all the wiring, but he only speaks Sumerian. You'd like to keep using him, because he really is a great electrician, but it's a big hassle teaching all the rest of your crew and your architects to speak Sumerian so they can talk to the guy. No matter how you try, it turns out Sumerian isn't a particularly good language to discuss complex wiring for modern housing projects (no words in Sumerian for "electricity" or "WiFi") so there are lots of errors in the work.
All the rest of your crew are young, very smart workers who are super at using smart phones and taking instruction from the automated processes your business uses. But they don't know how to do wiring, at least, not yet. In the choice between teaching the entire crew how to speak Sumerian or picking out a few of them and teaching them what they need to know about doing basic electrician tasks, it's smarter and more valuable to teach them the basics of being an electrician.