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The global generative AI art market is projected to grow at a compound annual growth rate of 40% through 2033, and its application in public art has rapidly diversified from facade projection to environment-responsive systems and citizen-participatory generative platforms. Yet systematic analysis of how generative AI is actually used in public space remains scarce. Adopting a single organizing axis—the source of input that drives real-time generation—this study reorganizes generative AI-based public art into four types: data-driven autonomous generation, environment-responsive installation, citizen-participatory generation, and artist–AI collaborative creation. The analysis reveals two distinct transitions. A medial transition, common to all types, replaces pre-rendered looping content with real-time, non-repeating generation through technological hybridity and temporal dynamism. A relational transition emerges as the dominant generative input expands from internal data toward environmental and human participation, thereby drawing audiences into the generative process and transforming one-way viewing into an interactive public experience (participatory engagement). The study thus positions generative AI as shifting public art from static display toward real-time, participation-based spatial experience, while raising new questions regarding authorship and the role of human participation in public art.