Thalassia, like all sea grasses, is a true plant unlike Caulerpa which is a type of algae. Caulerpa can release growth-inhibiting chemicals into the water to help it outcompete corals for space (much like many leather corals), though this can be negated by running carbon in your system. Much more worrying is Caulerpa's tendency to "go sexual" if it's not pruned regularly or it's stressed by low nitrates, when it will release its reproductive spores in one giant event clouding the tank water and possibly crashing the tank.
Thalassia, on the other hand, produces seeds though this is extremely rare both in captivity and in the wild. It also reproduces vegetatively by producing runners, a type of root that runs just underneath the surface of the sand that other stalks will grow off of. If you're familiar with freshwater plants, it works just the same as Amazon swords, microswords, hairgrass, and Vallisneria. It needs a deep sand bed, decent light, and does well with some flow. It's not nearly as hardy as some of the other macroalgaes but you'll never need to worry about it breaking up and colonizing your display or growing out of control. I'm not sure where you can get it locally but it shouldn't be too hard to get online.
