The photo shows the difference in the shape of the buds. The longer bud on the top (curved here, but sometimes straight) is blackhaw Viburnum. The stubby, grayish buds on the twig below are privet.
I was glad John persisted in his quest to find out which privet we have in central NJ. Having lived in the south, he at first assumed we have Chinese privet (Ligustrum sinense), but after posting a closeup of the flower on iNaturalist, he soon learned that we have Ligustrum obtusifolium, latin for border privet.
another closeup, John pointed out various identifying characters of border privet: "Corolla tubular with small lobes (the tube longer than the lobes), Shoots pubescent (i.e., NOT glabrous)"
The Penn State post describes "a gradient of four different species: border (L. obtusifolium), common (L. vulgare), Japanese (L. japonicum), and Chinese (L. sinense)." But John has determined that we only have border privet here, probably because it is the most cold-hardy. When I lived in North Carolina, we had a mix of Japanese and Chinese, with the Japanese having much larger and glossier leaves.
Thanks to Inge Regan and John Clark for these photos. Winter, by the way, is a great time to go after infestations of privet in the backyard or local woodlands. Come by Herrontown Woods on Sunday mornings after 10:30am and you'll likely see the Invasive Species of the Month Club clearing swaths of privet to make room for native species.