I stand by what I said earlier, a Ludwigia and probably a non-aquatic Alternanthera. The latter will not survive in an aquarium, but it makes for an excellent terrarium plant. If you pull it out of the tank and plant the stems in a pot, they may recover...
As for the Ludwigia, what you're calling "branches" are the petioles of the leaves. They may look like stems, but they're actually part of the leaf - specifically, the thin, stalk part of the leaf that attaches to the stem. Some Ludwigia species have longer petioles than others, and even within a species petiole length can vary widely (L. palustris is a particularly adaptable plant whose leaves are known to take many forms).
Originally Posted by Cavan Allen
Good answer. I think the first one looks more like palustris.
That was my gut reaction, too. I threw in repens as an afterthought, mostly on a hunch that the 2 plants came from the same source - IME, the shops that sell A. ficoidea for aquarium use aren't the type to carry anything but repens in the way of Ludwigias. But, who knows - the supplier might have made a substitution or something. The leaf shape does fit palustris better.