Zed's are for 'zones' -they are not airline or route specific. They are only zone and price specific.
Essentially, you buy a zed ticket that is good on any airline that will accept them. The further apart the 2 zones are, the more the Zed costs. Each zed comes in ZL, ZM, and ZH (L=low, M=medium, and H=high). The higher the zed, the higher the cost.
So, 3 issues for the user:
1) what zed has the airline you're planning to use negotiated with your carrier, and who are you (employee, spouse, child dependent, domestic partner, retiree, or registered guest)? Say United and Air China both fly Shanghai to LAX. Say you're a Air USA pilot. Well, Air USA has negotiated unlimited ZL for employees and ZM for dependents and parents with United, but ZH for employees (limited to 8 only) and no zeds for anyone else on Air China. So, on Air China, you can go, but nobody else can. On United, your family can go with you.
So, you've got the right zed fare. Now, issue 2, the zones:
2) The world is divided into zones. The further you go, the more zones. So, again, you're an Air USA pilot in Shanghai - how many zones did you pay for? Say it's 5 zones to go from Shanghai to LAX. It's 7 zones to go from Shanghai to IAD. If you've bought a 5 zone ticket, you can't get on the IAD flight, and only can go to an airport within 5 zones, say LAX, SFO, or Dubai, for instance). If you've got a 7 zone, you can go to IAD, or anywhere else within the 7 zones or less, including LAX, ORD, JFK, or DFW.
3) cashing them in. If you buy 1 ZH (high cost) for 7 zones, that can take you all the way from Shanghai to the US East coast on any airline (in my example). It can also take you from Shanghai-LAX, or even BOS-LGA. But once you 'cash it in' by giving it to an agent, you can't really get it back. So, say you're in Shanghai again. There's a United flight to Tokyo which looks iffy, but the loads are good on United to both LAX and IAD from Tokyo. If you've only got 1 '7 zone ZH', you can't split it into 2, one for the Tokyo flight and one for the LAX flight. Furthermore, once you 'list' for the UA flight, you are essentially stuck on UA. If you miss that UA flight, you can't easily get that '7 zone ZH' back from UA and go use it on Air China. So don't give it up unless you're sure you're gonna' get on.
So, the prudent zed traveler buys a couple based on what the flights look like. For 'family in Bankok': (note, the zone #'s I'm using and the ZL,ZM, or ZH I'm using are all hypothetical. Check to find the correct amount of Zones you need, and check with Delta to find out what Zed agreements they have with the various carriers you might use, such as Korean, ANA, Japan Air, Thai Air, Cathay, Singapore, etc). Maybe a 8 zone ZH for that Bankok-anywhere in the US flight so that you're good to go if you need it. Maybe a 6 zone ZM to go direct from Bangkok-LAX on the carrier that takes ZM's with Delta (why pay the ZH price when all you need is a ZM). Maybe a 3 zone ZL to go on XYZ Airlines to Singapore, Hong Kong or Tokyo (2 zones) or Seoul (3 zones, which is why you buy the 3, so you can use it to Seoul OR Tokyo/Singapore/Hong Kong), then a 6 zone ZL from Singapore/Tokyo/Hong Kong or Seoul (Tokyo/Hong Kong only needs 5 say, but again, you buy 6 so you can use it from Seoul/Singapore OR Tokyo/Hong Kong) to get you back to the USA on United if your airline's flight from Tokyo (which you plan to non-rev on) suddenly oversells. If you have enough $ to buy separate zeds for Seoul, Hong Kong, Singapore and Tokyo (likely different zones) than that would be even better, but most guys can't carry a couple grand in zeds, even if they are refundable, so they buy less, and pay for the 'worst case' scenarios (Seoul to NYC or a ZH direct to NYC or anywhere else in the US from anywhere in Asia) rather than the best case (ZL to Tokyo/Hong Kong, another ZL to LAX or SFO).
When you get back, you refund all the zeds you didn't use.
Most counter agents don't know zeds in the US. Either buy them @ an employee travel office in the hub, or internationally, where most of the agents know zeds better b/c they deal with them more often (just don't ask them about jumpseating!).
Sorry for the length. Good luck.