Tesla (TSLA -3.48%) CEO Elon Musk made a big claim at the company's Autonomy Day in April, telling investors to expect a million self-driving taxis on the road sometime next year. That's really ambitious, even by Musk's standards.

Tesla was supposed to put a fully self-driving vehicle on the road by 2017. It missed that deadline, and don't be surprised to see it missing the next one as well -- Musk's plan to put so many robotaxis on the roads in the space of just eighteen months will hit regulatory hurdles, along with competition from Alphabet (GOOG -0.86%) (GOOGL -0.83%) subsidiary Waymo's slow but steady steps to expand its own ridesharing business.

Person reading a book inside a self-driving car.

Image Source: Getty Images

Waymo makes actual progress while the Tesla news circus continues

Alphabet's self-driving division Waymo has been a leader in the autonomous driving space. Its cars have racked up millions of miles on public roads, leaving the others way behind.

So it was logical for Waymo to commercially launch its self-driving service in the Phoenix metro area late last year. However, the commercial launch of the Waymo One self-driving taxi service came with certain limitations, such as a requirement that a test driver be present and that operational ability be limited to a fixed radius.

Despite having a massive technological lead over rivals, Waymo decided to play it safe in the beginning. So Musk's belief that Teslas will soon start driving themselves all on their own by next year -- helping owners make as much as $30,000 a year by renting out their vehicles -- seems far-fetched.

The National Highway Traffic Safety Administration (NHTSA) says that fully automated safety features can be expected in cars only after 2025. This seems logical, as autonomous cars will have to undergo extensive testing before they are deemed fit to drive autonomously -- after all, there will be lives at stake when cars start driving on their own.

But Tesla hasn't tested its self-driving vehicles extensively just yet like Waymo has done. And Tesla cars don't have an impeccable safety record either: The cars have been involved in fatal crashes, even with the autopilot system engaged.

This is why expecting Tesla to get a green light from regulators to get a million robotaxis on the road by next year is likely nothing more than a pipe dream. But we can't say the same for Waymo -- the Alphabet subsidiary now seems to be on track to expand its robotaxi business thanks to its latest partnership.

Alphabet takes another step toward monetizing its autonomous tech

Waymo has expanded its self-driving taxi program in Phoenix by tying up with Lyft. The ridesharing company's customers can call for a Waymo self-driving car using Lyft's app, though there will be safety drivers behind the wheels of those cars.

The service is limited for now, as only 10 Waymo vehicles are available for Lyft customers in selected towns around the Phoenix area. But despite its limited scope, this is a big step forward because it shows us the future of the self-driving industry.

One of the biggest challenges that the likes of Lyft and Uber face is keeping their drivers happy. Uber recently cut driver compensation by 25%, and has reportedly been blocking drivers' accounts. Given that Uber reportedly loses an average of 58 cents on each ride, it is probably being forced to take steps to cut costs.

Reducing drivers' pay is one way these ridesharing companies can achieve that. But such a move is bound to run into opposition, as the recent driver strike shows.

This is where Waymo comes into play with its self-driving taxis. It can tie up with more ridesharing companies, supplying them with autonomous vehicles that could drive on their own and take the human element out of the equation.

Not surprisingly, Waymo is now looking to set up a factory in Detroit to make self-driving cars, which could be considered a precursor to a wider launch of its robotaxi service.

Tesla, on the other hand, has a much simpler plan -- sending a software update to its cars to equip them with self-driving capabilities. Musk believes he can leapfrog the others in autonomous driving tech with such a move. But don't be surprised if Waymo, with its slow and steady approach, takes the cake by tying up with the very companies that Musk plans to compete against.