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.”