i think Rhoeo (Tradescantia spathacea) is very common in the tropics - it withstands very harsh hot sun. i've seen it used as ground cover in scorching mexico. and as it happens, i just put up a multi-plant pic with it - it was wedged high in the tree - so probably birds seeded it. it's ubiquitous in south fl - it grows in the ditches! it's a WEED!
so, obviously plants sold in nurseries might be hybridized to look prettier (as your striped one), but they're obviously related. so they use the same name for all kinds of similar hybrids, but actual plants might differ quite a bit and be a bit more touchy compared to the original.