This is a plant (not an orchid) which I considered a weed when I grew orchids in Hawaii because it was EVERYWHERE! Here in Texas, I think it makes a great terrarium plant because it is attractive and grows VERY fast. I have it growing in my terrariums with the roots directly in water, but I have seen it growing outside just on the outside of my patio growing as a small, squat little thing in the Texas heat. When growing 'wild' it sticks to the areas that are shady. You can see TINY pink flowers on the last pic.
Thanks! I posted this question to Facebook and I got the answer Pilea microphylla. I believe I have found the name I've been searching for.
For what its worth, I highly recommend this species for terrarium growers who are looking for an ornamental plant that is attractive, grows quickly and absorbs nutrients to combat algae growth.