  In 2006, Balan/Casazza/Edidin \cite{BCE} introduced the frame theoretic study
of phaseless reconstruction. Since then, this has turned into a very active
area of research. Over the years, many people have replaced the term {\it
phaseless reconstruction} with {\it phase retrieval}. Casazza then asked: {\it
Are these really the same?} In this paper, we will show that phase retrieval is
equivalent to phaseless reconstruction. We then show, more generally, that
phase retrieval by projections is equivalent to phaseless reconstruction by
projections. Finally, we study {\it weak phase retrieval} and discover that it
is very different from phaseless reconstruction.
