Just to add to what nony said, if the schools do follow up on your application, HR does keep a record of the reason you left, and whether or not it was on "good terms."
For an employer, a layoff is not a bad reason, but a termination is going to raise flags (even if it was just because the job was a bad fit for you or your performance didn't meet expectations). It will also raise flags if you said in the app that you resigned for another opportunity when in reality your position was eliminated in a layoff.
I'm guessing it will be similar for schools, but I'm also guessing they're less likely to do full verifications on every applicant. Safe bet is to be accurate.
(Applications Advice, Letters of Recommendation . . . )