The statement that you want to talk to an attorney is sufficient for Miranda. It conveys the information that you don’t want to answer any questions without legal guidance. It doesn’t matter at that time if the attorney is the public defender or Zimmerman’s attorneys.
I believe what was stated above was, however, “MY” attorney. One would hope not to make technically nonsensical statements though some flustering is understandable at the time. And “AN” attorney might mean they then call the county prosecutor to greet you... it really should be in logic “an attorney of my choice.”
Also the attorney means you want to be able to litigate...?