Do we say expiry date or expiration date?

Both are correct — 'expiry date' is standard British English (also common in Canada, Australia, India), while 'expiration date' is standard American English. Same meaning, zero difference in substance: the date after which something is no longer valid.

Usage notes: British English happily uses 'expiry' as a standalone noun ('the expiry of the lease'); American English prefers 'expiration' there too. In technical and legal writing both appear, and abbreviations like 'exp. date' are universal on cards and packaging.

Pick whichever matches your audience and stay consistent. What matters far more than the word is the behavior around it: businesses lose real money not from spelling expiry wrong, but from not writing the date down anywhere it will be seen again before it passes.