Brooklyn Botanic Garden
The New York (Bronx) Botanical Garden

The New York Botanical Garden was founded by the the Torrey Botanical Club and Nathaniel Lord and Elizabeth Britton in 1891, though the history seems to be in dispute. The garden was primarily a scientific and educational catalog, “a place of agreeable public resort” was its secondary purpose. The Torrey Botanical Club also contributed to the Brooklyn Botanic Garden’s Herbarium in 1897.

But I still have no idea why one is Botanical and the other Botanic.