My local farm supply told me the other day (when I was buying my pumice, and asking about DE), that although the terms can and often are used interchangeably, a lot of folks in his industry use the term "diatomaceous earth" to describe the powder form, and "diatomite" to describe the larger particles we use as a soil medium. I've heard both terms, but always use DE, since that's what EP Minerals calls the 25 lb. bags of medium-coarse stuff that I buy from O'Reilly Auto Parts.
My teacher used to always call it Axis, because that was a brand name he bought.
I'm not a pedant, so I wouldn't get hung up on the wording, but it did occur to me that searching for diatomite might produce some other sources that folks would otherwise not find when looking for agricultural diatomaceous earth, so I thought I'd share that.