Tilia americana (smaller, redder twig above) and Tilia cordata (larger, grayer twig below) IDed by buds only. I’m not confident that I’ve got the right species but I’m quite sure that the genus is correct. Neither twig looks quite like they’re supposed to, but I found these twigs already broken off. I attribute their unusual shape and slightly unusual coloration to the fact they have been disconnected from their corresponding tree. Note that the difference in size is not because of different species, but just because the americana twig happened to be from a sub-branch.
The americana ID is corroborated by the NYC tree map.