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The answer is easy: none.
The difference in names seems to be discipline specific, as does interpretation. Health and behavioral researchers seem more prone to talk about logistic regression, and they are also more likely to interpret coefficients in terms of odds ratios. Economists, political scientists, and many sociologists seem to prefer talking about logit models, and they are also more likely to interpret results in terms of predicted probabilities. The preference for referring to logistic regression as logit is likely due to the fact that the term fits in nicely with other commonly used methods in these disciplines, such as probit and Tobit models.
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