You are correct that "narrow tailoring" and "least restrictive means" are often treated as synonyms.1
For example, Professor Volokh describes narrow tailoring as having four components: advancement of the compelling governmental interest, no over-inclusiveness, the least restrictive alternative, and no under-inclusiveness.2 However, he says that the first "three components are closely related, and all of them could be subsumed within the 'least restrictive alternative' inquiry."3
The Supreme Court has sometimes equated strict scrutiny with the "least restrictive alternative" formulation, saying, "Unquestionably we have held that a government practice or statute which restricts 'fundamental rights' or which contains 'suspect classifications' is to be subjected to 'strict scrutiny' and can be justified only if it furthers a compelling government purpose and, even then, only if no less restrictive alternative is available."4
The court has also distinguished between narrow tailoring and a "least restrictive alternative" test, at least with respect to laws that infringe on speech: "Lest any confusion on the point remain, we reaffirm today that a regulation of the time, place, or manner of protected speech must be narrowly tailored to serve the government's legitimate, content-neutral interests, but that it need not be the least restrictive or least intrusive means of doing so."5. The dissent in that same case described the majority's view as a "serious distortion of the narrow tailoring requirement", and said, "Our cases have not, as the majority asserts, 'clearly' rejected a less-restrictive-alternative test. [...] The Court's past concern for the extent to which a regulation burdens speech more than would a satisfactory alternative is noticeably absent from today's decision. The majority requires only that government show that its interest cannot be served as effectively without the challenged restriction."6.
Some statutes remove any ambiguity, prescribing the "least restrictive alternative" test.7.
In summary, certain areas of law (free speech, religious freedoms, affirmative action) have their own idiosyncratic treatment of strict scrutiny, narrow tailoring, and the "least restrictive alternative" test. It is always best to read the particular line of case law in the field you are interested in to see exactly what formula the court has established in that area.
1. Winkler, Adam, Fatal in Theory and Strict in Fact: An Empirical Analysis of Strict Scrutiny in the Federal Courts. Vanderbilt Law Review, Vol. 59, p. 793, 2006; UCLA School of Law Research Paper No. 06-14. At 800: "Narrow tailoring requires that the law
capture within its reach no more activity (or less) than is necessary to
advance those compelling ends. An alternative phrasing is that the
law must be the “least restrictive alternative” available to pursue those ends."
2. Eugene Volokh, Freedom of Speech, Permissible Tailoring and Transcending Strict Scrutiny, 144 U. Pennsylvania L. Rev. 2417 (1997).
4. Regents of Univ. of California v. Bakke 438 U.S. 265 (1978) (Opinion of Justice Brennan, Justice White, Justice Marshall, and Justice Blackmun, concurring in the judgment in part and dissenting in part.)
5. Ward v. Rock Against Racism 491 U.S. 781 (1989)
7. The Religious Freedom Restoration Act, implemented in part in 42 U.S.C. §2000bb-1(b): "Government may substantially burden a person’s exercise of religion only if it demonstrates that application of the burden to the person is in furtherance of a compelling governmental interest; and is the least restrictive means of furthering that compelling governmental interest."