Media firms are flocking to the new Instagram Stories, and that includes many of the same companies that are part of select group of publishers creating content for Snapchat Discover.

Since Instagram introduced Stories less than two weeks ago, a flurry of media companies including CNN, Food Network, People, Comedy Central, Cosmopolitan and Tastemade have taken to regularly producing Stories, and some say they are seeing solid early viewership numbers. AwesomenessTV, which caters to teens and tweens, has even run one of the first ads on the platform.

The stars of Comedy Central's “Broad City” appearing in an Instagram Story. Photo: Instagram

Instagram, the photo-sharing app owned by Facebook, has acknowledged the new function owes a great deal of inspiration to Snapchat. In fact Instagram CEO Kevin Systrom noted that Snapchat “pioneered” the stories format in an interview with the Wall Street Journal last month.

Instagram Stories, like Snapchat Stories, typically consist of a handful of images and videos—often annotated and decorated with graphics and emoticons—stitched together in a single package. Both are generally shot with a person’s phone and disappear after 24 hours.

But they differ from the more professionally produced Snapchat Discover, which allows a limited list of approved media partners to post scheduled, pre-produced collections of content that often features unique Snapchat-esque animation.

Since Instagram Stories launched Aug. 2, Time Inc. has been aggressively testing it, particularly with coverage of the Rio Olympics. For example, its brand Sports Illustrated has been posting images from various Olympic venues to Instagram Stories. Entertainment Weekly is planning to use the format on Friday to reveal this week’s cover featuring “Fantastic Beasts” star Eddie Redmayne. Earlier this week, People produced an Instagram Story from Rio with members of NBC’s “Today” show, including Hoda Kotb, that generated over 100,000 views, according to a Time Inc. spokeswoman.

An image from a recent Instagram Story for People Photo: Instagram

Publishers say that overall the new content is very experimental, but the possibilities are intriguing. For example, Tastemade, which already has 2.1 million followers on Instagram, produced a “Breakfast Around the World” Instagram Story via which staffers from the company’s offices in Brazil, Argentina, the U.K., Japan and the U.S. shot small video segments with local digital influencers highlighting a local breakfast cuisine.

“You can do an orchestrated story, with a definite start and finish,” explained Oren Katzeff, head of programming at Tastemade. “That is different than an individual piece of content in a feed.”

Instagram Stories are designed for less-polished and less-perfected content, which is also an appeal for publishers. Users don’t even have an option to like the posts, removing some of the pressure.

“What we like so far is that Instagram Stories gives us the ability to showcase content that might not have made it into our highly curated feed before,” said Amy Odell, editor of Cosmopolitan.com. For example, she said, “instead of just one perfectly edited image of an ice cream sundae, we posted several Stories from a recent ice cream social held at Cosmopolitan.com headquarters.”

Cosmopolitan is one of several Hearst brands experimenting with Instagram Stories. Travel + Leisure recently created a “frosé tasting” Story which generated 106,000 views.

The fact that Instagram is showcasing Stories along the top of a user’s feed at the moment is helping to drive early consumption, publishers say. Mashable’s first Instagram Story generated approximately 30,000 unique viewers, more than double what the site sees on an average video posted to Instagram, said a spokesman. Similarly, Food Network says that its Stories have regularly exceeded 100,000 views and that the audience is being accumulated much faster than the network’s average Instagram post.

Instagram's new Stories feature Photo: Instagram

Instagram Stories are different from Snapchat Discover in many ways, including that Discover partners—which are top media companies—are featured on a dedicated portion of the app. Photo: Snapchat

Publishers say that Instagram has provided solid access to data and measurement early on. But unlike the average Instagram post, Instagram Stories aren’t necessarily designed to be shared—whereas Snapchat Discover content can be shared within Snapchat.

“The content is supposed to be more transient, things that you may not want to save forever,” said Peer Schneider, general manager of IGN, a site for gaming enthusiasts.

Of course, comparing Instagram Stories with Snapchat Discover is a bit apple and oranges. Both apps claim huge daily audiences: Snapchat reaches 150 million people a day, while Instagram says it reaches 300 million daily users. Snapchat Discover, however, provides a unique, stand-alone section of its app specifically to showcase media partners’ content, and Snapchat delivers ads into Discover content that either Snapchat or the partners can sell.

Right now, Instagram doesn't offer a formal ad product for Stories, though the company says that is in the works. Instagram hasn’t really put in place limitations for publishers when it comes to branded entertainment, allowing AwesomenessTV to publish a series of videos and images produced on behalf of Old Navy—a campaign titled “Best Day Ever.”

AwesomenessTV ran an ad for Old Navy on its Instagram account. Photo: Instagram

“Every day we’re engaging Gen Z on the platforms they care about, and Instagram Stories was a game changer,” said Paul Kelly, AwesomenessTV’s chief partnerships officer. “To Old Navy’s credit, they were totally up for experimenting with us. And, the response to [the Old Navy] campaign has been phenomenal.”

Write to Mike Shields at mike.shields@wsj.com