A fecal test cannot differentiate intestinal blood from blood from red meat.
A fecal test cannot differentiate intestinal blood and blood from red meat.
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As you can see from JSBangs response (which I think misinterprets what your sentence means), neither of those phrasings are clear, even though they are technically correct; they are fairly ambiguous as written.
Assuming I am parsing your sentence correctly, I would suggest that the clearest way to phrase this is as follows:
A fecal test cannot differentiate between intestinal blood and blood from red meat.
(Since between implies exactly two items, a reader knows to parse the words that follow as two items and nothing more.)
Or, one of these two might be even clearer, if the specific phrasings are acceptable:
- A fecal test cannot differentiate between blood from intestines and blood from red meat.
- A fecal test cannot differentiate between intestinal blood and red-meat blood.
The advantage of these latter two sentences is that the similar structure of the two compared items makes it easy to understand what you are comparing.
Both of these are correct:
A fecal test cannot differentiate intestinal blood from red meat.
A fecal test cannot differentiate intestinal blood and red meat.
However, I'd say that the first is clearer and should be preferred.
Both of your example sentences are very unclear, though, because I'm not sure what's being differentiated here. Are we doing a three-way comparison between intestinal blood, blood, and red meat? If so, I would suggest the following:
A fecal test cannot differentiate between intestinal blood, blood, and red meat.
There is a slight difference in the emphasis when you use the two forms. When differentiating intestinal blood from meat blood, it seems, to me, to acknowledge that meat blood is a high probability event but possibly just an example of a false positive when it's intestinal blood you're looking for.
In the idiom, "he doesn't know me from Adam," it's clear that I am the thing that we're talking about identifying/differentiating/distinguishing. That's not so clear if I say, "he couldn't distinguish Adam and me" and I don't think it's just because it's an idiom. I think that the first thing is what we want to identify. The second is just an example of potential confounds.