STEUBENVILLE, Ohio — Philosophical differences between the top two Republican presidential candidates are becoming starker as Rick Santorum drives harder on religious and social issues that Mitt Romney rarely discusses in detail.

In recent days, Santorum has questioned the usefulness of public schools, criticized prenatal testing and said President Barack Obama's theology is not "based on the Bible." On Monday, he likened Obama to politicians who spread fear about new oil-extraction technologies "so they can control your lives."

The remarks contrast sharply with Romney's even-tempered emphasis on jobs, the economy and his resume as a can-do corporate executive.

The differences give Republican voters clear choices to shape their party's identity and image heading into the fall battle against Obama. They also will test whether social conservatives and tea partyers can outperform the GOP establishment in key states such as Michigan and Ohio.

Both men campaigned Monday in Ohio, where their audiences, styles and messages produced distinctly contrasting atmospheres.

Santorum, the former senator from Pennsylvania, appeared in Steubenville before a packed room including many students and employees of the town's Franciscan University. In his hour-long talk, Santorum never mentioned Romney or Newt Gingrich, who campaigned in Oklahoma.

He aimed squarely at Obama as he discussed abortion, marriage, the church and family. When he touched on non-social issues such as energy and the environment, he couched them in terms of epic struggles between reasonable conservatives and radical, sometimes devious Democrats.

"I refer to global warming as not climate science but political science," Santorum said to loud applause. He said Obama has "radical environmentalist policies" that reject robust extraction of oil and gas from many U.S. areas, including the Arctic National Wildlife Refuge in Alaska.

In Cincinnati, on the opposite side of the state, Romney hit Santorum's spending record as a member of Congress but stayed away from the former senator's recent comments on social and other hot-button issues.

"One of the people I'm running against, Sen. Santorum, goes to Washington and calls himself a budget hawk. Then after he's been there awhile says he's no longer a budget hawk," Romney said. "Well I am a budget hawk."

"When Republicans go to Washington and spend like Democrats, you're going to have a lot of spending, and that's what we've seen over the last several years," Romney added.

Santorum said Obama and his allies want to frighten people about alleged dangers of petroleum-extraction techniques, including hydraulic fracturing, or "fracking," which might lower energy prices. He said these officials seek to "get your dollars, turn it to politicians who can win elections so they can control your lives."

"Understand what's at stake, folks," Santorum said. "It's your economic liberty. It's your religious liberty. It's your freedom of speech." He said government has accumulated power "by weakening the institutions that people rely upon in their lives."

Santorum said those institutions include: marriage, which is hurt by the so-called "marriage penalty" in tax policy; the Roman Catholic Church, which he said is under assault by Obama's policies regarding contraception coverage in health care plans; and charities, which he said would suffer if Obama succeeds in ending the tax deductibility for charitable donations.

"It's not surprising to see the president's assault on, first, charities," Santorum said.

It's not unusual for the GOP to face intra-party struggles between conservatives focused largely on social issues such as abortion and school prayer, and those focused mainly on financial matters such as spending and taxes. Sometimes the quarrels become loud and problematic, as when Pat Buchanan called for a "culture war" at the 1992 Republican national convention. President George H.W. Bush, already facing troubles, lost to Bill Clinton that fall.

Santorum, a devout Catholic, clearly welcomes the renewed emphasis on social issues generated in part by the flap over contraception policies at Catholic-affiliated institutions and the quarrel between Planned Parenthood and the Susan G. Komen for the Cure breast cancer charity.

Even with some polls showing Santorum surging, however, Romney has stuck with the same style and message he has used for months. The former Massachusetts governor sells himself as the efficient CEO who will fix the economy. He makes little mention in his standard campaign speech of the social issues that increasingly have dominated Santorum's events.

Romney, who is Mormon, has pushed a petition aimed at ensuring "religious liberty" and criticizing the Obama administration for requiring health plans to cover contraception, even at Catholic hospitals that oppose birth control.

He rebuked Santorum during a campaign rally in Boise, Idaho, last week but focused strictly on Santorum's spending record in Congress. In several recent stops in Michigan, Romney did not mention Santorum.

Romney's campaign schedule has stayed largely the same. He holds relatively few traditional campaign events in a day. Monday, for instance, Romney held one event to Santorum's four in two states.

Romney spends significant time making phone calls and raising money, a vital task in which he outpaces his opponents.

His public events are aimed mostly at generating local media coverage. By rarely taking questions from his traveling press corps, Romney has avoided being dragged into issues such as Santorum's claim that Obama's theology is not Bible-based. (Santorum later said he did not question that Obama is a Christian.)

His target audience is the business wing of the Republican Party and most of Romney's campaign events are held at factories or outside small businesses, giving him the opportunity to highlight his economic credentials. Romney has used the strategy since Iowa. Monday's event was held at Meridian Bioscience, a Cincinnati-based medical device maker, where Romney addressed a handful of employees and toured the factory.

Romney advisers say they aren't changing the messaging strategy they believe has worked in other states. Holding small events allows the campaign to reach local media and show that Romney is putting in time in the state. Romney held a series of rallies in South Carolina only to lose, and switched back to holding smaller events leading up to Florida's primary, which he won.