The short answer
New Mexico is tricky because people use the same words for very different products. Ojo Caliente is a natural mineral resort. Riverbend is a riverside hot springs lodging property in Truth or Consequences. Ten Thousand Waves is a superb Japanese-style spa near Santa Fe, but not a natural geothermal hot spring.
The useful booking decision is not which resort has the prettiest marketing page. It is whether you want a destination mineral resort, a private-pool couples stay, a Santa Fe spa night, or a budget hot springs town. Sort that first, then compare rooms.