Naive Bayes and Logistic Regression can both produce a...

The difference is generative versus discriminative. Naive Bayes models the joint distribution P(x, y) by estimating P(y) and P(x|y) under a strong conditional-independence assumption between features given the class, then uses Bayes’ rule to get P(y|x). Logistic Regression skips the joint distribution entirely and directly models P(y|x) by fitting weights that separate the classes.

Because Naive Bayes only estimates per-feature conditional distributions rather than jointly optimizing a weight vector, it needs far fewer training examples to reach its asymptotic error — it converges in roughly O(log n) examples versus O(n) for Logistic Regression, so on small datasets Naive Bayes often wins even though its independence assumption is almost always wrong. As data grows, Logistic Regression’s ability to learn feature interactions and correct for correlated features via its jointly-optimized weights lets it overtake Naive Bayes and reach a lower asymptotic error, especially when the independence assumption is badly violated. The practical heuristic: small, high-dimensional, sparse data (text classification with limited labeled examples) favors Naive Bayes; larger datasets where you can afford to fit interactions, or where features are strongly correlated, favor Logistic Regression.