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.