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Sponsored search is a key revenue source for search engines, where advertisers bid on keywords to target users or search queries of interest. However, finding relevant keywords for a given query is challenging due to the large and dynamic keyword space, ambiguous user/advertiser intents, and diverse possible topics and languages. In this work, we present a comprehensive comparison between two paradigms for online query rewriting: Generative (NLG) and Dense Retrieval (DR) methods. We observe that both methods offer complementary benefits that are additive. As a result, we show that around 40% of the high-quality keywords retrieved by the two approaches are unique and not retrieved by the other. To leverage the strengths of both methods, we propose CLOVER-Unity, a novel approach that unifies generative and dense retrieval methods in one single model. Through offline experiments, we show that the NLG and DR components of CLOVER-Unity consistently outperform individually trained NLG and DR models on public and internal benchmarks. Furthermore, we show that CLOVER-Unity achieves 9.8% higher good keyword density than the ensemble of two separate DR and NLG models while reducing computational costs by almost half. We conduct extensive online A/B experiments on Microsoft Bing in 140+ countries and achieve improved user engagement, with an average increase in total clicks by 0.89% and increased revenue by 1.27%. We also share our practical lessons and optimization tricks for deploying such unified models in production.