Does the term "Biophysics" have two different meanings?
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 &amp; methods):  


Issues in psychophysical measurement  
Spatial hearing: the psychophysics of human sound localization 


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


Psychophysics: Method and theory


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.