This is my first post, so hoping I can get some help (and that I am doing this right).
My husband and I recently bought a new house without landscaping. To our luck, a nursery nearby was going out of business and they were selling ALL of their plants for 1 dollar. We got these plants and originally thought they were hawthorne, but as they continue to develop we are not so sure. If you have any ideas, I would greatly appreciate the advice. They seem to be growing better on the back side of the house where the soil is dry and hard, but don't appear to be developing as well (although they are not dying-they just seem thinned out) on the front side of our house where the soil is more of a damp clay. If it helps at all, we live in the Georgia/Florida line and these plants were being grown at a local nursery, however there was not any identification (or anyone to help with identifying them) when we bought them from the closing nursery.
To me this looks like a beach plant. A clue might be in whatever develops from the little white buds I see in the picture. Clip off a small portion with the buds included and go to another nursery that is still in business. If you find anyone knowledgeable there, they might help you identify it, plus guide you towards something that will thrive in your type of soil and situation (sun or shade). Ask them who their resident expert is.