Elnina, the one in your photo is also
L.lucidum, notice the stiff leaves with the pronounced crease. They grow to be very large, I had a huge one that was cut down about five years ago, and I'm still finding seedlings from it.
http://www.floridata.com/ref/L/ligu_luc.cfm
Japanese Privet
L.japonicum is one of the least invasive privets in my opinion, and the only one I'd recommend anyone actually plant. They usually have softer leaves with a more rounded tip, and they generally don't produce as many berries.
https://plants.ces.ncsu.edu/plants/a...rum-japonicum/
Chinese Privet
(L.sinense) is by far the WORST one of all. They have small dull one inch leaves, and it's the one you see invading the entire southeast, particularly moist bottomland type areas.