As explained in the answer, almost always Expedia will issue a single ticket across one or more airlines (the technical term for that is "interlining"), which is different from an itinerary made up of actually separately issued tickets.
In the former case, there's always exactly one airline responsible for getting you to your destination in case of a missed connection or itinerary changes; in the latter case, you're often on your own.
What Kiwi.com is doing with their "separate tickets plus connection insurance" model is called "virtual interlining", and it's an interesting alternative in some scenarios (well-connected airports with many alternatives). But I'd still never risk it on an important connection.
I've had a very bad experience with Kiwi.com myself: I booked a Ryanair flight on them without realizing that Ryanair is actively trying to prevent Kiwi from reselling their flights. Kiwi.com apparently works around this by booking tickets on pools of Ryanair retail accounts, to which they don't share the credentials with travelers – making mobile check-in impossible. (And Ryanair at least at the time was charging over 100€ of a "service fee" for a boarding pass print at the airport...)
This is only marginally related to booking separate tickets, but I suppose the larger point is that it's never a great situation to be stuck between the lines of two companies actively hostile towards each other, when you really depend on their cooperation to get to your destination.
"Official" interline agreements are an explicit statement that two or more airlines will make at least some reasonable effort to get you and your luggage to your destination, and will be on the hook for it (under ICAO regulations) if things don't work out.
> in the latter case, you're often on your own
If so why would you want this? Isn't the Expedia way of issuing a single ticket better?
You never want that, but sometimes you can't get the other way.
According to the poster, he found a combo that wasn't available in the online booking system. From what I recall from my time at Travelocity (coming onto 20 years ago, so probably slightly out of date), there are only a handful of GDS 's(Global Distribution Systems), of which Sabre - the owner of Travelocity - was at the time the largest. Those GDS systems are supposed to know about all of the flights from all of the airlines and find the cheapest route across all airlines and for a long time, they did. But as time went on, carriers like Southwest refused to participate with the GDS's and offered direct fares to customers while competitive GDS's sprang up and started to fragment the ones that were being used.
I can't recall exactly which GDS Expedia used (Worldspan or Galileo I think), but I do remember that you could comparison shop between them and us and find lower fares depending on which GDS you were using because they listed some airlines that we didn't and vice versa and even some fares on specific airlines - Sabre was originally an AA subsidiary so tended to have better access to AA fares and was _always_ the cheapest way to fly in or out of Dallas.
So what OP is looking for is what the GDS's would call an uber-GDS - which is, of course, what all of them are angling to become, but are being thwarted by competitive business practices. It's entirely possible that he found a route that was partly available on Sabre and partly available on Expedia that was cheaper than what was available on either, but he had to go poking around for it.
So, why not make a GDS of GDS'es that searched all of them and found combinations like the one OP found? A lot of companies tried - sites like Travelocity and Expedia and Orbitz were online and scrapeable, after all. The problem was, there was no money to be made in them. Travelocity made a lot of its money through travel agency fees - Travelocity acted as a travel agent and got the same commission on tickets that a brick and mortar travel agent would get. I assume Expedia and Orbitz and Priceline did the same. The aggregators, on the other hand, had to charge a fee on top of that to make their site profitable. There are a few people like OP who have a specialized need to be in a certain place at a certain time that an aggregator of aggregators could come up with, but not enough that were willing to pay a fee on top of the combined flight. In addition, savvy travlers could search the aggregator... and then go book the individual flights directly on the travel sites (you couldn't do this with GDS flights, at least not back then).
So yes, Expedia's way is better, and the best option in 99% of cases. It'd be great if the airlines would play ball to give consumers what they wanted, but... well, good luck with that.
I used Kiwi.com for this a few weeks ago (combining multiple European carriers, including Ryanair) and it worked rather well.
My first flight was delayed, and it seemed likely I would miss the second leg flight, so they sent me an email with a list of options to reschedule. I'd purchased the 'Premium Protection', so I think I could choose a new option up to €250 (+ hotel if overnight) without paying any extra.
I decided to risk taking the first flight, as the second airport was much bigger so figured there would be better flights from there. Fortunately the flight on the second leg was delayed too, so I didn't need to change anything.