Wrong.
Ordinals are a made up convention for looking at Bitcoin txns.
Inscriptions are the data packed into a txn's witnesses which are associated with sats tracked via the ordinanal convention.
Discussion
If i download just Bitcoin core do i have ordinals?
Ordinals isn't a piece of software or a feature... It's a convention - think of it like a way to count. So yes, if you just download core and know the convention of ordinals you have everything you need to use ordinals and inscriptions