I don't know how many of the airlines use the same program, but it would make sense for them to, & it's my understanding that that program was "Dining a la Card" (www.dalc.com). Before learning of the "true identity" of the program being used as a mileage partner w/ my carrier, I had (over the past few years) received occasional direct mail pieces for the Dining a la Card program. Membership cost $50 & one received a 20% discount/rebate for dining at participating restaurants (w/ various restrictions).
An aside: I was curious to know how the cost of the program's "rebate" compared re: 20% vs. 10-miles-per-$. I used a cost of 1-cent-per-mile for the sample calculation (I know that it doesn't necessarily represent reality, & that it can vary...it was simply a reasonable ballpark estimate). For a $100 purchase, the % rebate would = $20 . If miles were awarded, the rebate would = 1000 -- which could cost the program anywhere from less than $10 to $20 max (I can't imagine miles costing them more than 2-cents per, particularly given the enormous volume which they purchase from their respective airline affiliates), which would seem to indicate that the cost of "rebating" in the form of miles is possibly more cost-effective for the program (realizing, of course, that there are several other $-related variables involved in administering miles vs. $).
Anyway, I learned in the past few minutes (when I popped over to wwwdalc.com) that the Dining a la Card program is now subsumed w/i "iDine Prime" (www.idineprime.com). I perused the info on the site, & one program change which is noteworthy is the fact that they now allow rebates for multiple visits to the same restaurant w/i the same month (limit still = $600 spent, but it is allowed to be reached w/i multiple visits vs. the former restriction of a single visit). Only a subset of participating restaurants allow the multiple visit exception (the program labels them w/ a "Diamond" on the web site / the restaurants w/ the rebate-for-first-visit-per-month only restriction are labelled w/ a "Star").
The iDine rebates for "Diamond" restaurants are in the form of $, @ least...I'm very curious to know whether the next quarterly update received for various airline-affiliated versions of the program will cite a new benefit re: multi-visit-w/i-the-same-month mileage earning potential for the "Diamond" restaurants.
The former Dining a la Card site & the iDinePrime site both provided the ability to search for a participating restaurant by city, which was useful. Note, however, that in my experience, neither the airline-program-specific published directory issued quarterly nor the online searchable database included all participating restaurants (e.g. I ate @ a restaurant that was not in either directory, was happily surprised to see miles posted to my acct, & then saw said restaurant listed in the next quarter's hard copy directory / a call placed to the program's customer service # revealed that the restaurant in question had been a participant for 5 years). If one wants to be certain as to whether a restaurant which is not listed in either directory participates (& particularly restaurants known to be part of a chain or otherwise operated by the same company & having a restaurant affiliated w/ such listed but others not), I would advise calling the customer service # (particularly if it's a restaurant you would be going to regardless of whether they were affiliated--their membership in the program may result in one subsequently choosing to restrict the purchase to only specific [enrolled] credit cards).
In my experience w/ the airline-affiliated program, my miles have posted regularly, & the one time I had miles missing, a call to their customer service # resulted in a prompt correction (miles posted w/i 2 wks) & courteous voicemail message (w/i days of the call) informing me of the correction having been implemented & a callback # for a specific representative should I have any questions or problems regarding the miles posting.
Word of advice: do not use a to-be-enrolled card the day you call in to have it enrolled--give them @ least 24 hrs to process the enrollment, or be prepared to send a hard copy of your receipt in to obtain mileage credit (does it sound like I learned this the hard way?

). When I enrolled my first card, I asked when it would be "ready" & was told "by 6pm tonight" (for my time zone)...the miles didn't post...I called...I was told that it's best to give them 24hrs.
They have definitely added restaurants to the program over the past year. What turned me off of the program when I had received the direct mail pieces was the paltry choice I seemed to have for my area (the provided list was either incomplete &/or they simply didn't have many restaurants in my area @ the time [& not many that were very appealing to me]). The restaurant list I saw in the direct mail piece left me w/ the impression that only crappy restaurants participated. I know now that there are some terrific restaurants in the program (including many for which one likely wouldn't leave the premises w/o spending @ least $30 per person).
At least once every few months, my co-workers & I go out to lunch @ a particular restaurant which is a relatively new participant in the program. My co-workers know I'm a mileage maniac & thus aid in my endeavor by allowing me to charge the entire lunch on one of my enrolled cards (it's a hassle sorting out the cash [there seems to always be someone who tries to screw anyone charging an overall dining expense], but it's worth it, overall). On days when we go as a group & don't happen to go to the aforementioned restaurant, my co-workers get a laugh out of my response to any in transit restaurant-identification inquiry of "where should we go?"...I whip out the latest quarterly hard copy directory & ask aloud whether anyone has ever heard of ___ (I go through a list of nearby restaurants w/ which I am unfamiliar [if nothing else, I learn how to "correctly" pronounce various strangely named entries...

]).
The bottom line is that it doesn't cost any $ to enroll in the airline-affiliate version of the program...decide where you want the miles, in case you do happen to stumble upon or otherwise plan to obtain miles as a result of dining @ a particular restaurant, & enroll accordingly.
Note that enrollment in the program(s) can produce a "side-effect" whose nature can vary btwn "disappointing" & "exceeding all expectation": knowing that one can obtain miles for dining @ particular restaurants, one is "susceptible" to unplanned pursuit of 10-miles-per-$ dining when one is undecided as to where one will be dining & has no discernable preference...trying a restaurant about which one knows nothing can turn out to be wonderful, or suck...

I do know that the "sting" of the cost of some meals @ a particular restaurant which is among my favorites is definitely soothed by the mileage "balm" which follows...
Lastly, I am unaware of whether gift certificate purchases @ participating restaurants qualify, but if they do, that's yet another avenue of closing an I'm-this-close-to-a-free-trip mileage gap (relatively time-sensitive or otherwise) w/o having to purchase miles from the airline. On a related note, the use of a mileage-earning dining program could be particularly useful for adding miles to frequent flyer accts associated w/ airlines one no longer flies or flies infrequently enough to make an award earning timeframe seem interminable [dine your way to the rest of an award!

]).
BTW, the mileage-earning aspect of such a dining program has actually had me thinking @ times of approaching the management of some of my favorite restaurants to ask (w/ an ulterior motive, of course) whether they've ever heard of Dining a la Card (now iDinePrime) & whether they'd consider joining (w/ my carefully & strategically educating them on the bordering-on-the-obsessive tendencies of the many mileage maniacs lurking about [I see one every day in a mirror

]). I've never followed up on the lark-like thinking I've just described, but the fact that I even *think* about it says "something" (scary-?), I know...