The second sounds like the "least restrictive means" standard set by the RFRA--the one the HHS rule at issue in Hobby Lobby failed to meet. The first sounds like the language of rational basis review--but courts do not apply the rational basis test in abortion cases.
In Casey in 1992, the Court established a new, sort of squishy standard, under which laws restricting abortion before the fetus was viable were constitutional as long as they did not impose an "undue burden" on the mother's right to terminate her pregnancy. This relaxed (a lot) the "strict scrutiny" standard the Court had applied in Roe v. Wade, when it declared abortion to be a fundamental right.
But Casey did not go so far as to apply the very relaxed "rational basis" standard in determining whether abortion laws are constitutional. The Court is no longer willing to claim abortion is a fundamental constitutional right, and under the "undue burden" standard state laws can restrict it pretty sharply without violating the Constitution. The laws requiring women to be given certain information before they receive abortions, which seem to have the Satanists' panties in a bunch, are an example of this.