But the two businesses have different long-term visions for how they fit into the larger educational universe.
"We're really trying to disrupt higher education," said David Stavens, who co-founded Udacity in June 2011 with Sebastian Thrun and Mike Sokolsky.
Stavens, who has a doctorate in computer science from Stanford, said top-tier universities offer a valuable experience for those who can afford it but that "there are many institutions, particularly down-market institutions, that charge fantastic fees for education but then deliver a substandard education."
While Udacity is focusing on skill-building courses such as computer science in the short term, the company has greater ambitions, Stavens said.
"Down the road ... we aspire to be a complete university, offer courses in every discipline and then degrees," he said.
Coursera co-founders Daphne Koller and Andrew Ng, both current Stanford computer science professors, struck a more accommodating tone than Stavens.
"Our goal is to broaden access to higher education for anyone with a computer and an Internet connection, not to displace existing universities," Koller and Ng wrote in a joint email.
And unlike Udacity, Coursera does not have the long-term goal of becoming a stand-alone university.
"We believe the best teaching lies at existing universities," they said, adding that schools could benefit from using a "flipped classroom model" in which students watch lectures on their own time and use class time to ask questions and solve problems.
The companies' relationships with universities further amplify their different visions.
While Udacity hires professors who teach their courses at schools such as Stanford and the University of Virginia, it has no official relationships with any colleges.
Coursera, on the other hand, currently has formal agreements to offer classes from 33 schools, including Stanford, Duke University, University of Michigan and Hebrew University of Jerusalem.
Both companies' founders were involved in and inspired by the popularity of three online computer-science classes Stanford offered for free in the autumn of 2011.
Udacity co-founder Thrun, known for his work developing self-driving cars at Google and Stanford, taught the artificial intelligence class.
Stavens, who helped Thrun put the class online, said they expected to get a few hundred students.
"About 160,000 enrolled in over 195 countries," Stavens said, "and then we really saw the opportunity to offer massive, open, online classes."
At the same time, Ng was teaching the machine-learning course, which he said had 100,000 students.
Given the background of the founders, it isn't surprising that computer science features heavily in both companies' course offerings. Sixty-seven of Coursera's 200 courses and 15 of Udacity's 18 classes are in the subject.
Stavens said constant innovations in technology made the courses relevant even for people who already have gone to college.
"I have three degrees in computer science, and in all honesty my skills are already out of date because the last time I took a class the iPhone didn't exist," Stavens said.
Despite being competitors, Stavens said Udacity benefits from the established institutions' involvement with Coursera and from Harvard's and MIT's joint edX nonprofit because they raise the credibility of online learning.
But he expressed skepticism that brick-and-mortar institutions built on "high fees and exclusivity" would ever offer credentials or degrees for online work, which would cost a fraction of the tuition paid by on-campus students. Doing so would undermine their own business models.
"If you want to fundamentally change education, you have to be prepared to certify your students. ... Industries very rarely disrupt themselves from the inside," he said.
Currently, both Coursera and Udacity offer electronic certificates to students who complete courses, but neither can verify the identity of the person taking the online final exam. Udacity recently signed an agreement with testing center company Pearson VUE to allow students to take tests in physical testing centers. Stavens said the ability to verify the identity of the test taker will make it hard to dispute the validity of a student's exam results.
Udacity's business model is based on generating revenue from referrals of students to potential employers.
Koller and Ng said that while Coursera is not currently enacting revenue-generating strategies, it is also considering implementing an employer-referral system.
Corbin Tarrant, an independent technology consultant from Michigan, said he has completed courses at both Coursera and Udacity.
Both sites have been an improvement over his experience taking online courses at DeVry University, where he earned a bachelor's degree in Computer Information Systems in 2006, he said.
"There's better technology; browsers have improved," Tarrant said. "There weren't even lecture videos on the DeVry online courses. ... It's a more varied experience."
He has considered going back to school to earn a second bachelor's or master's degree. But for now he's chosen Udacity, Coursera and other online education like P2PU.org because he "saw the potential to learn all this stuff without spending tons on tuition."
And for now the lack of credentialing isn't a huge concern for him.
"The particular classes I've been taking have been to improve my skills as a programmer and get more programming jobs. ... I don't really need a degree for that if I can show people what I'm doing," he said.
Emanuele Santoro, a 20-year-old software developer in Italy, has also taken courses from both companies.
"I can really appreciate that I can pause and rewind the professor," he wrote in an email.
He said Coursera has an advantage over Udacity in terms of number of courses taught but that he found Udacity courses more engaging.
"I see professors taking part (in the online) forum very often," he wrote.
Besides offering more classes, Coursera has received more money from investors than Udacity. New Enterprise Associates and Kleiner Perkins Caufield & Byers have provided $18.5 million in Series A funding, Koller and Ng said.
Udacity has received $5 million from Charles River Ventures, according to Stavens.