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SAN FRANCISCO — Three years ago, Steve Jobs compared personal computers to trucks and tablets to cars. PCs will still be around, he said, but more people will want tablets.

Apple on Tuesday took another step toward making that prediction come true. It souped up its iPad tablets with faster processors and zippier connections.

The company upgraded its iPad Mini, the smaller tablet, with a higher-resolution display. The full-size iPad with a 9.7-inch screen was renamed the iPad Air, because it has a slimmer design and has lost some weight. The small iPad starts at $400 and the bigger iPad will cost $500. Both iPads will ship in November.

“This is our biggest leap forward ever in a full-sized iPad,” said Philip W. Schiller, vice president for marketing at Apple, at a company event here.

Jobs, who died in 2011, declared at a business conference in 2010 that the era of the personal computer was nearly over. He said that tablets, which are more portable and easier to use, would cut people’s ties to old-school computers, relegating PCs — like trucks — to carrying the heaviest loads.

“When we were an agrarian nation, all cars were trucks, because that’s what you needed on the farm,” Jobs said. As cars became faster and easier to use, trucks became passé, he said.

Tablets are already devouring the PC market. About 120 million tablets were shipped in 2012, nearly seven times as many as in 2010, when the Apple iPad was first released, according to Gartner, a market-research company. IDC, another research company, predicts that sales of tablets will surpass those of PCs in the fourth quarter of this year, and on an annual basis in 2015.

The new iPad Mini gained a high-resolution Retina display. It costs $400 — $70 more than the previous iPad Mini. But Apple said it would continue selling the older iPad Mini for $300.

The iPad Air is about 20 percent thinner than the previous iPad and weighs one pound, down from 1.4 pounds.

Both new iPads will include new chips, called A7 and M7, which Apple introduced in its latest high-end iPhone last month. The A7 is a faster processor with a new architecture that makes it better at multitasking. The M7 is a separate chip dedicated to sensing movement, which could allow for new capabilities in software or games that incorporate motion, like a racing game.

Both iPads will also include an improved antenna system for faster Wi-Fi connections. They will come in silver and gray. The iPad Air goes on sale Nov. 1, but the new Mini will ship later in November, suggesting that supply is limited for the smaller tablet.

The new iPads do not include the fingerprint sensor technology, TouchID, that Apple introduced in the high-end iPhone 5S. Analysts think that may be because parts are in limited supply, since the iPhone 5S is selling so quickly.

Mac computers have taken the back seat of Apple’s business, with most of Apple’s profit coming from iPhones and iPads. The company said that, beginning Tuesday, it would make its new Mac operating system, Mavericks, available free.

Apple also released upgrades for some of its Mac hardware on Tuesday. The MacBook Pro notebooks with Retina displays are now thinner and faster, with better battery life. The 13-inch version will cost $1,300 and the 15-inch model will cost $2,000.

Apple also said the high-end Mac desktop computer, the Mac Pro, which was introduced in June, would begin shipping in December, for $3,000. It will be assembled in the United States.

Although the tablet market is growing quickly, tablets are not nearly as ubiquitous as smartphones. Gartner said that manufacturers would ship 1 billion smartphones and 184 million tablets this year. Carolina Milanesi, a Gartner analyst, said smartphones were probably more popular because the phone function makes a smartphone a necessity, while a tablet is considered a device that is just nice to have.

Jobs was wrong about one thing regarding tablets. In a conference call with investors in 2010, he mocked smaller tablets, calling them “dead on arrival” and saying they would need to come with sandpaper so people could sand down their fingertips to use them.

For Apple’s competitors, smaller tablets are getting the most traction, partly because of their lower costs. And that also appears to be the case for Apple. Since the release of the lower-cost iPad Mini late last year, the average selling price of iPads overall has fallen, according to the company’s financial reports, meaning that the iPad Mini is most likely outselling the bigger iPad.

Apple is No. 1 in the tablet market with about a 32 percent share, according to IDC. But Apple faces fierce competition from companies like Amazon, Samsung Electronics and Google, whose tablets undercut the iPad in price. Samsung, the No. 2 tablet maker, is quickly gaining traction, with 18 percent of the market in the second quarter, up from 7.6 percent in the period a year earlier, according to IDC.

Milanesi, of Gartner, said she expected smaller tablets to continue gaining in popularity as the smartphone market becomes saturated.

“We expect this holiday season to be all about smaller tablets as even the long-term holiday favorite — the smartphone — loses its appeal,” she said.