as mentioned above, air-breathing missile is an older term, started way back in the early 50’s with the Regulus and similar programs. Now, replaced by cruise missile (AGM) in all texts and dialogs.
ABM is used for anti-ballistic missiles, starting back in Reagan’s time for the protection systems installed up north around the North Dakota and Wyoming missile and B-52 bases.
Reagan’s Star Wars defense systems were designed from the ground-up (including space-based systems and ground-launched systems) to upgrade and replace the much earlier anti-air missile systems like Nike, Nike-Ajax, Nike-Hercules, etc, but the Army’s new ABM capacity for its THAAD missile and Patriot defense systems (and the similar Navy’s AEGIS ABM upgrades) are up-rated (missile altitude, missile weapons, launch controls and launch responses and response speed, in-course tracking, fuzes, etc.) from the original THAAD and Patriot and AEGIS anti-air defenses.
But the up-rated THAAD and AEGIS changes use designs and sensors and controls and guidance inventions started from Reagan’s programs.
That ABM system was before Reagan.
The Safeguard system, consisting of the Spartan (high altitude) and the Sprint (low altitude) missile systems were operational from Fall of 1975 and deactivated in very early 1976.
The only part of the system that was built and operational was in North Dakota and the Montana (not Wyoming) site was never completed.
We still use the Perimeter Acquisition radar site to track space objects.