word choice - What is the difference between tori vs. dori?

In Aikido, different dojos seem to latch on to using either dori or tori when describing grabbing attacks. For instance one dojo might say:

Katate Dori

Another would say:

Katate Tori

Each dojo will profess that their way of saying / spelling it is the more traditional and correct. Is there a difference between these two similar terms, and if so which one is more correct for denoting a grab?

Answer

I know very little about Aikido and can only explain general facts about the Japanese language.

“Tori” and “dori” in these example are the noun form of the verb toru (取る; take, grab). In isolation, this noun form is read as “tori.”

Both Katate Tori and Katate Dori are compound words made of katate (片手; one hand) and tori. However, in Japanese, the first consonant of the second component of a compound word is often changed as k→g, s→z, t→d and h→b. This phenomenon is called rendaku (連濁). Note that I said “often,” not “always.” If rendaku occurs in your case, the compound word becomes Katate Dori. If not, it becomes Katate Tori.

There are some patterns when rendaku tends to occur and when it cannot occur as is explained in Wikipedia, but there is no absolute rule that explains everything. In the case of katate + tori, it is certainly possible to have rendaku here, so Katate Dori is a possible form. But this does not mean that rendaku must occur, so the form Katate Tori is also possible.

Often only one form survives and the other form dies out, in which case we can say that one form is correct and the other is incorrect in the modern language. In some cases, the version without rendaku and the version with rendaku both survive but mean different things. For example, both yamakawa and yamagawa are compound words made of yama (山; mountain) and kawa (川; river), but yamakawa means mountains and rivers whereas yamagawa means a river in a mountain.

But in your case, it seems that both forms are used in the same way judging from several webpages in English I found by web search. (I checked the pages in English because it is difficult to search this in Japanese, because when written in Japanese, both become 片手取り, as Andrew stated in his answer.) From this, I see no evidence that one is “more correct” than the other, whatever “more correct” means.