These 2 words are synonyms. The noun SPROUT has 2 meanings: 1. any new growth of a plant such as a new branch or a bud 2. a newly grown bud (especially from a germinating seed) • SPROUT (verb) The verb SPROUT has 2 meanings: 1. produce buds, branches, or germinate 2. put forth and grow sprouts or shoots --------------------------------------------------------------------------------------------- The verb burgeon [ also spelt bourgeon] means: 1. a. To put forth new buds, leaves, or greenery; sprout. b. To begin to grow or blossom. 2. To grow or develop rapidly.