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1.

Some sources (including the current Tag-info at biology SE) state; biophysics is the adoption of techniques / methodologies from physics to study biological systems.

The use of methods from the physical sciences to aid in the study of biological systems…

Bio-SE- Tag .

Biophysics or biological physics is an interdisciplinary science that applies the approaches and methods of physics to study biological systems…

Wikipedia (permalink).

Biophysics — the branch of biology that applies the methods of physics to the study of biological structures and processes…

Dictionary.com


2.

According to other sources, biophysics is the subject concerned with how the laws or phenomena of physics work in living systems.

“The subject of biophysics are the physical principles underlying all process of living systems.”

Google Book: Biophysics, An introduction, By Ronald Glaser (permalink).

Biophysics is a bridge between biology and physics. ... Biophysics looks for principles that describe patterns. If the principles are powerful, they make detailed predictions that can be tested. ---

Biophysical society


These two, although apparently quite similar (and I agree, have overlapping areas) basically indicate completely different things.

The first group of definitions refer to techniques and methodologies; such as “how does an electron microscope work?”, or “what could be the best strategy to separate membrane-lipids?”, or “how could you identify cells with the expression of certain RNA”; etc.

The second group refers to the physical principles applicable to living systems. Such as “why do phospholipids form a bilayer?” or “how do brain waves reach the scalp?” or “how does a humming bird move its wings when it hovers in a stationary manner?” or “what are the mechanisms working in the path of transport through phloem?”.

Now my question is: Is there a dual and different meaning, or use of the term ‘biophysics’?

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    $\begingroup$ You may be thinking of "techniques and methodologies" too narrowly. It doesn't mean just the experimental techniques and methods but the mathematical techniques and theoretical frameworks as well. For example applying the theoretical framework of statistical mechanics to understanding molecular models. When you expand your notion of "technique and methodologies" to include those as well, the two definitions seem more in-synch. $\endgroup$ – Charles E. Grant Apr 8 '17 at 17:41
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In brief, you are correct. Although there may be a spectrum of uses, the sources that you quote illustrate two distinct meanings for the term, ‘biophysics’. Your interpretation of the first class is a little off-target (see comment by Charles E. Grant) but, in essence, you have answered your own question.

What is there to add? Perhaps, “Don’t judge a book by its cover”.

You may not be aware of the factors leading to the naming of new ‘disciplines’. Although they arise as the result of genuine developments in existing disciplines, the need for a name to be distinctive and attractive (for a new chair, society, journal or course) may outweigh considerations of accuracy. And once the name is coined, anyone can confer it on their own newborn, or discover that they were a systems biologist or a practitioner of translational medicine all along. And nobody will sue you for saying you are a molecular geneticist, even if you have no idea what a backcross is.

So what about biophysics?

In fact it would seem that the main usage is in the first sense defined in your question. Although the physicist, Max Delbrück, made a major contribution to ‘biology’ his initial motivation — that processes in living organisms might require new physical insights to explain them (biophysics in the second sense of the question) — was not borne out by his subsequent studies. It is ironic in this context that the institute he established at the University of Cologne did not bear the name ‘biophysics’, but ‘molecular genetics’, and the institute named after him in Berlin bears the name ‘molecular medicine’ (Max-Delbrück-Centrum für Molekulare Medizin) — whatever that may mean.

It is worth looking inside the covers of the Biophysical Journal to see what biophysics is in practice. The contents of the first and subsequent issues indicate a focus on electrophysiology, photosynthesis and the use of different types of electromagnetic radiation and spectroscopic techniques to study biological systems. A more recent issue is much wider in scope, but is subdivided mainly on the basis of the biological system being examined. As mentioned, the fit is more with the first sense of the use of ‘biophysics’ in the question.

Finally, I note that one of the first university departments to bear the moniker ‘biophysics’ — ‘The Astbury Department of Biophysics’ at the University of Leeds (1962) — was named after William Thomas Astbury, who studied X-ray diffraction of fibres, notably wool. However, it has since been renamed ‘The Astbury Centre for Structural Molecular Biology’. How fickle is taste!

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Short answer
Biophysics encompasses the study of biological systems in physical terms and the methods involved to achieve that goal.

Background
I'll approach this question first from the area of research I'm actively involved in at the time of this writing -

Psychophysics is

[...] the scientific study of the relationship between stimuli (specified in physical terms) and the sensations and perceptions evoked by these stimuli. The term psychophysics is used to denote both the substantive study of stimulus-response relationships and the methodologies used for this study.

source: (RIT)

In short this would translate as

The study of the sensation and perception of physical stimuli and the methods involved to accomplish this.

To illustrate I will cite the titles of two well-read articles in this area highlighting the dual use (study & methods):

And to illustrate a compelling example that merges both uses in one:

Now to your question; I've done electrophysiology which might, arguably, be considered biophysics, but I'm less comfortable in the arena of biophysics. But given my reasoning above, you can safely replace Psycho with Bio and say that Biophysics is

The study of biological systems in physical terms and the methods involved to accomplish this.

For example, the University of Wisconsin describes it as:

[B]iophysics combines state-of-the-art physical measurements with computational models to understand the detailed physical mechanisms underlying the behavior of complex biological systems.

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