Samsung Electronics Co. unveiled targets for making its most advanced chips, detailing for the first time how its production road map would compare with that of Taiwan Semiconductor Manufacturing Co. in their closely watched technology race.

On Monday, Samsung’s contract chipmaking unit said it would start manufacturing chips on the 2-nanometer production process in 2025 and the 1.4-nanometer production process in 2027. That advances from its current 3-nanometer chip production that began in June and which the company called an industry first.

That timeline is similar to TSMC, which had said it would start mass production of 3-nanometer chips later this year and subsequently introduce other variations. By 2025, it will also move into the 2-nanometer process. It hasn’t detailed its plans beyond that time.

TSMC and South Korea’s Samsung are the only two companies now with the finances and technological prowess to manufacture the world’s most sophisticated chips that would help advance technologies such as artificial intelligence systems and autonomous cars.

The road map targets signal how quickly and reliably next-generation semiconductors will become available, a key indicator for the most lucrative customers such as Apple Inc. or Nvidia Corp. that must adjust their own pipelines based on anticipated progression in chip-production technologies. They book orders months, if not years, in advance.

TSMC enjoys a wide market share lead over Samsung, which makes most of its profits from memory-chip sales rather than its contract manufacturing, or foundry, business. But foundry customers worry about an overdependence on the Taiwanese chip maker, given its market dominance and recent geopolitical tensions amid Chinese displays of military power around the self-ruled island.

“Everyone would like a second vendor on top of TSMC, but that depends on Samsung’s ability to keep up,” said Handel Jones, chief executive of International Business Strategies, a chip-industry consulting company.

More customers have shown a heightened interest in “dual sourcing” alongside TSMC, Kang Moon-soo, executive vice president of business development at Samsung’s foundry business, said at a media briefing ahead of the Monday road map unveiling.

A TSMC spokeswoman declined to comment.

Chipmaking processes carry a numerical label that loosely denotes the size of the transistors that can be packed on a chip. The lower the nanometer number, the more advanced the technology. The technological leaps promise faster computing power, better battery performance and more. The latest iPhones use 4-nanometer chips made by TSMC.

TSMC and Samsung stand at the final stretches of a multidecade pursuit of miniaturizing chip circuitry and harnessing new production techniques. And further progress in the space hangs on these two Asian chip makers, said Dale Gai, a Taiwan-based research director at Counterpoint Research.

“The industry wants to see Samsung and TSMC continue to extend Moore’s Law so they can continue to make plans for their next products,” said Mr. Gai, referencing the industry’s long-running prediction that the number of transistors packed onto a chip would double every year or two.

Intel Corp. also desires to become a bigger player in advanced chipmaking, both as an in-house producer of its flagship PC processor chips and as a manufacturer for other companies’ semiconductor designs. In recent years, the U.S. chip maker has fallen behind in technology by several generations to TSMC and Samsung. Catching up will take years, industry analysts have said.

Intel Chief Executive

Pat Gelsinger laid out a plan last year to regain the company’s edge by moving faster than it has in the past on new generations of chips that pack in more transistors. Last week, he said at a company conference that his aim to make five leaps forward in transistor technology in four years was on, or ahead of, schedule.

TSMC leads the overall foundry space covering all generations of chips with about 64% market share compared with 15% for Samsung, according to International Business Strategies’ projections for 2022 that forecast total industry revenue at roughly $117 billion. The foundry business should grow aggressively through the end of the decade, with estimated revenues of $303 billion in 2030, IBS predicts.

In the most advanced parts of the foundry market, or chips made with the 5-nanometer process or smaller, TSMC’s projected market share this year is 90% versus Samsung’s 10%. If Samsung can successfully deploy its next-generation technologies without missteps, its share could double to 20% by 2026, according to IBS.

Samsung is aggressively investing with hopes of shrinking that gap with TSMC. The South Korean company is building a $17 billion chipmaking plant for its foundry business in Taylor, Texas, and has floated the prospect of investing nearly $200 billion in 11 new chipmaking plants in Texas over the next two decades. TSMC last year pledged to spend $100 billion by 2024 on factory expansions.

One advantage that TSMC enjoys beyond its massive customer base is being able to “serve the client rather than compete with them,” said Tadahiro Kuroda, a University of Tokyo professor who works with TSMC on semiconductor research and development projects in Japan.

In contrast, Samsung operates its own chip-design unit and is the world’s biggest maker of smartphones and TVs, putting it in direct competition with clients such as Apple that rely on contract chip makers.

At a company symposium in August, TSMC Chief Executive C.C. Wei said he was confident in the company’s future 2-nanometer technology.

“I can guarantee you all that it would then be the technology with best (transistor) density and performance,” Mr. Wei said.

—Asa Fitch in San Jose, Calif., contributed to this article.

Write to Jiyoung Sohn at jiyoung.sohn@wsj.com and Yang Jie at jie.yang@wsj.com