A Blue Origin rocket heads for a successful landing after an unmanned suborbital test flight from its West Texas launch site on Nov. 23, 2015 in this screen grab from a Blue Origin video.

A reusable-rocket milestone has sparked a mini-squabble between two of the billionaires who are helping transform the private spaceflight industry.

On Monday (Nov. 23), Blue Origin — a company established by Amazon.com founder Jeff Bezos —launched a rocket into suborbital space and then brought it back down for a soft landing at a pad in West Texas. The uncrewed test marked a big step toward full rocket reusability, which could open the heavens to human exploration by dramatically lowering the cost of spaceflight, Bezos said.

"To be able to do a vertical landing with a fully reusable booster stage is a really big deal," he said during a press briefing Tuesday (Nov. 24). "It is the Holy Grail — to get full reuse." [See more photos of Blue Origin's epic test flight]

Billionaire Elon Musk, who founded the private spaceflight company SpaceX in 2002, congratulated Bezos and Blue Origin via Twitter Tuesday. But he also mentioned the suborbital nature of Monday's test and said Blue Origin did not exactly make history.

"But credit for 1st reusable suborbital rocket goes to X-15 ‪en.m.wikipedia.org/wiki/North_American_X-15 … And Burt Rutan for commercial ‪en.m.wikipedia.org/wiki/SpaceShipOne … ," Musk tweeted, referring to the U.S. Air Force/NASA X-15 experimental rocket plane and SpaceShipOne, the Rutan-designed craft that reached space twice in the span of two weeks back in 2004.

A little context here: SpaceX is also working hard to develop reusable, vertically landing rockets. Indeed, the company's Grasshopper prototype landed successfully multiple times during flight tests over the last few years, though it never came close to reaching space.

SpaceX has also brought the first stage of its Falcon 9 rocket back for a soft "ocean landing" in the Atlantic during orbital launches, and nearly succeeded in landing the booster on a floating ocean platform on two other orbital flights. (Both times, the rocket stage hit the target but came down too hard and exploded on the uncrewed ship's deck.)

In another tweet Tuesday, Musk stressed how much tougher it is to get to orbital rather than suborbital space.

"Getting to space needs ~Mach 3, but GTO [geostationary transfer] orbit requires ~Mach 30. The energy needed is the square, i.e. 9 units for space and 900 for orbit," Musk tweeted.

In Tuesday's press briefing, however, Bezos pushed back against some of Musk's statements, saying that what Blue Origin just accomplished isn't all that different from what SpaceX is trying to do on its orbital flights.

"You have to remember, SpaceX is only trying to recover their first-stage booster, which is suborbital. The second point that I would make is that the SpaceX first stage does an in-space deceleration burn to make their re-entry environment more benign," Jeff Bezos said. "So if anything, the Blue Origin booster that we just flew and demonstrated may be the one that flies through the harsher re-entry environment. And then finally, the hardest part of vertical landing and reusability is probably the final landing segment, which is the same for both boosters."

Bezos and Musk have both said they aim to help humanity become a truly spacefaring species, with a permanent presence on Mars and other off-Earth locales. Maybe a little healthy rivalry between the two will help these big dreams become a reality.

"This is a good marker for everyone in the industry, and it's going to push everyone in the industry even harder," Eric Stallmer, president of the Commercial Spaceflight Federation, said of Blue Origin's test flight.

"I think it's great that there's healthy competition out there among a lot of these entrepreneurs," Stallmer told Space.com. "I think that's a fantastic thing for the industry, because I think, in the end, it's going to be the consumer who wins."

Follow Mike Wall on Twitter @michaeldwall and Google+. Follow us @Spacedotcom, Facebook or Google+. Originally published on Space.com.