The Cosmic Jackpot by George O. Smith appeared in the October 1948 issue of Thrilling Wonder Stories.
The Cosmic Jackpot opens with a confused and angry Martian scientist receiving a red lipstick and a couple of worthless silver slugs in his change from a vending machine.
Meanwhile, on Earth, a scientist/entrepreneur has just announced the official roll-out of his commercial service: a point-of-sale matter transportation device. Simply put in your money, tell the machine what it is you want, and the good folks down at the warehouse will atomize your order and send it to you ASAP. So, like a cross between the replicators on Star Trek and Amazon Same Day Deliver. Except something goes wrong. When the scientist punches in an order for a lipstick for his dame during a demonstration for investors, rather than a lipstick, he gets an odd canister and some coinage of unknown origin!
Yep, the newly developed technology on earth is interfering with the commercial matter transfer vending machines on Mars. It only happens when the earthman and the Martian use the machine at the exact same moment; of course, they’re both determined to get to the bottom of what’s going on, so they doggedly use their machines over and over again until they are able to use the machine simultaneously at regular intervals.
The two men learn about each other’s worlds via the cheap and strange trinkets they send one another, from toys to postcards to starlet magazines. Each has to build their impression of the other on what they’re able to send and receive. Just as the earthman had been certain there was no possible intelligent life on Mars (too dry!), the Martian was certain that there was no possible intelligent life on Earth (too wet!); one of the best moments was the Martian’s fear and revulsion at a postcard of humans splashing about in the water on the Atlantic City beaches (that one went in the fireplace).
Eventually, both men send over bottles of air and are set to send themselves to the other’s world via the machine’s product return/refund mechanism. The earthman gets there first, just in time, too, since the Martian is about to be arrested for having fed slugs (the US dimes) into the machine.
Again, we have an idea piece, where the story revolves tightly around the concept, which is not so much the matter transmitter but the limitations of trying to learn about another culture through its commonplace artifacts. If you had to convey the entirety of what it is to be a human living on earth via stuff you could send them out of a Sear Catalog, what would you send?