Final answer:
Renaissance Platonism is distinguished from ancient Greek Platonism by the term 'Neoplatonism', which represents a synthesis with Christian ideology and other philosophies, emphasizing mathematics in understanding the universe.
Step-by-step explanation:
A modern term that distinguishes Renaissance Platonism from its Greek antecedents is Neoplatonism. This movement began with Plotinus in the 3rd century AD, revitalizing Plato's ideas by integrating them with concepts from other philosophies, including Christianity, Judaism, and the metaphysical ideas of the Stoics. Neoplatonism had a substantial impact on the intellectual landscape of the Renaissance through figures like Marsilio Ficino and Nicholas of Cusa, who combined its principles with Christian teachings and a mathematical understanding of the universe, respectively. Reflecting this synthesis, Neoplatonism influenced many aspects of Renaissance culture, including art, science, and the broader philosophical discourse of the time. Hence, the key differences lie in the synthesis with other philosophical and religious systems and an emphasis on mathematical understanding of the universe.