Large language models (LLMs) trained on web-scale corpora can memorize sensitive training data, posing significant privacy risks. Differential privacy (DP) has emerged as a principled framework that limits the influence of individual data points during training, yet the relationship between differential privacy and social bias in LLMs remains poorly understood. To investigate this, we present a systematic evaluation of social bias in a pretrained LLM trained with DP-SGD, comparing a DP model against non-DP baselines across four complementary paradigms: sentence scoring, text completion, tabular classification, and question answering. We find that DP reduces bias in sentence scoring tasks, where bias is measured through controlled likelihood comparisons, yet this improvement does not generalize across all tasks. Our results reveal a discrepancy between logit-level bias and output-level bias. Moreover, decreasing memorization does not necessarily reduce unfairness, underscoring the importance of multi-paradigm evaluation when assessing fairness in LLMs.