At the risk of playing layperson biochemist, here is as I understand it as of now.

rt-PCR and Abbott ID Now are both NAATs (nucleic acid amplification test)
rt-PCR is a generic term for a (reverse transcriptase–polymerase chain reaction (RT-PCR), and takes time and sending to a lab.
Abbott ID Now is a brand name for an rt-Isothermal test, and is rapid and done at doc/pharmacy usually.

SXM and France were specifying rt-PCR for their PCR level rules, but depending on who is reviewing it seem to accept the ID Now as equivalent to PCR - it is newer than rt-PCR, so probably not written into the rules.

Returning to U.S. requires a viral test (NAAT or an antigen), so either test or an antigen test within 3 days seems to comply. No antibody tests.

I appreciate hearing everyone’s experience, because at the end of the day, the rules are what’s happening on the ground!