So the plant in the foreground of the top pic is a hackberry, but the tree with berries in the background is a chinaberry (leaves and fruit both indicative of that species.) Chinaberry leaves and fruit turn yellow in the fall.
Chinaberry tree:
Chinese tallow (sometimes called chinaberry here is Texas) is a very different tree with heart shaped leaves and no large berry clusters like chinaberry has. Chinese tallow black fruits crack open and reveal white seeds in the fall and their leaves turn all kinds of different shades of yellow, red, and orange.
Chinese tallow:
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