Popper used testability, falsifiability and refutability interchangeably and presents it as a “criterion of demarcation”. (in “Conjectures and refutations” Page 53, lines 8-14)
He meant by that, a criterion for distinguishing scientific statements, from religious, metaphysical or pseudo-scientific statements.
The requirement that, any statement/ hypothesis/model/theory which claims to be scientific, should be testable, via empirical observations and if need be experiments.
Refutability and falsifiability:
However, the purpose of the testing is not to verify or confirm the hypothesis but to refute it (refutability) or falsify it (falsifiability).
Popper adds (in “Conjectures and refutations” Page 48, line 4):” A theory which is not refutable by any conceivable event is non-scientific. Irrefutability is not a virtue of a theory (as people often think) but a vice”
The “confusion” arises from the fact that the term, ”testability” had been used before Popper in a broader sense, one that stops at “verifiability”.
In restating the need for falsifiability, Popper insists that verifiability is not sufficient as criterion of demarcation between science and false science. He is redefining testability and giving it a narrower meaning.
Popper in my view rediscovered and restated in a clear manner what had been practiced by scientists since at least Newton, and had been proposed implicitly by early modern philosophers (see for example Francis Bacon, in Stanford Encyclopedia of Philosophy (on line), & 5).
In a sense, he restored testability to its original meaning i.e. refutability or falsifiability.
Some scientific theories contain their refutability criterion implicit in their counterintuitive predictions such as the predictions of time dilation, distance contraction or the bending of light by gravity, in the theory of relativity. Any failed prediction refutes, falsifies the theory.
In some cases, scientists themselves proposed a refutability criterion for their new hypothesis:
I quote Darwin for example (in ‘The origin of Species’, p190) :
“If it could be demonstrated, that any complex organ existed, which could not possibly have been formed by numerous, successive, slight modifications, my theory would absolutely break down” (end of quote).