celeriac and celery root are used interchangeably.
There are some particular varieties of celery that are bred to have a larger root, where a good sized root to be sold as celeriac is the main goal versus the stalks. Then there are others that are bred for the quality of the stalks. You can eat the top celery off a plant that was bred for celeriac, it generally won't be as nice. And you can dig up the root of celery that's grown for stalks, but it generally won't be nearly as big as one that's bred for the celeriac.
It's great stuff whatever it's called!
beets and swiss chard are sort of the same deal-eo, same plant, some are bred for the upper plant quality and some for the root quality.