The advent of LLMs has given rise to generative search, a new search paradigm in which LLMs retrieve information from the web related to a query and synthesize it into a single, coherent response. This paradigm differs fundamentally from traditional web search, where results are returned as a ranked list of independent web pages. In this paper, we ask: Along what dimensions does generative search differ from traditional search? We conduct a systematic comparison between Google organic search and five generative search systems from three providers: Google, OpenAI, and Perplexity. Our analysis reveals substantial variation among engines in their reliance on internal v.s. external knowledge, source diversity, and stability. While generative systems often achieve topical coverage comparable to traditional search, they do so using markedly different retrieval footprints and synthesis strategies. We further show that the outputs of generative search can vary across time and executions, raising new challenges for robustness. Our findings demonstrate that generative search introduces new dimensions that are not captured by existing evaluation paradigms, motivating the development of evaluations that explicitly account for retrieval behavior, synthesis, and stability in generative search systems.