well to me, in the second photo, the left plant looks like mondo grass, which isnt an aquatic plant. on the right, it looks like an anacharis plant, which is easy to take care of and may explain why it seems to be the only one thriving.
The second photo has two Mondo grass plants (Ophiopogon). In the mid-background on the right is a Bacopa (not an Anacharis, which IIRC is an old name for several plants in the Egeria and Elodea genera). You are right that Bacopa is the only one which will flourish underwater.
monnieri at a guess. It's actually also a bog plant, but one which will live indefinitely underwater. If it reaches the surface of an aquarium, it usually carries on growing