What my professors and administration told me:

Your NY State Teacher Certification has reciprocity in these states.  That means, with your license, you can teach in these states.

What that actually means, according to places where I’m trying to get a job:

Your NY State Teacher Certification has reciprocity here.  That means you don’t have to go to school again, that if you apply for a one-year license you’ll get it automatically, and that in that one year time span you can pay OUR state money to take OUR exams and get certified HERE.  And if someone with your same experience has our state’s certification, well, we’re more likely to take them over you, but you can still put in your resume!