B-HKD has provided a well written and accurate response.
Also noteworthy is that just because an aircraft is manufactured to ETOPS standards does not mean it is approved by the regulator to do so. That is a different process for the Ops Specs folks. However, for the USA, once ETOPS certification for an airframe (and pilot authorization) is attained, each individual flight must be specifically dispatched within an approved ETOPS parameter (120 minutes, 180 minutes, etc.). As a consequence, that flight must then also have an ETOPS Pre Departure Check accomplished be ETOPS certified mechanics/engineers. And there are additional procedures pilots must accomplish prior to entering ETOPS airspace.
ETOPS flights (beyond 60 minutes from nearest adequate airport) are being flown by 737-700s, 800s, and 900ERs today. And I suspect there will be more routes flown by these types in the near future.