Do the losses have the same meaning in these two mathematical expressions or not?
It is a mathematical convention. If you assume that the fields have exp[i(K*x-wt)] dependece then refractive index mush have a positive imaginary part (for passive media) (N=n+ik).
exp[iKx] = exp[i*N*w*x/c] = exp[i*(n+ik)*w*x/c] = exp[i*n*w*x/c] * exp[-k*w*x/c]
The field magnitude should drop in a lossy material as the wave propagates from left to right and thus the sign of exp[-k*w*x/c] is correct. (n,k>0)
Where K = N*w/c is the wavevector and w is the angular frequency.
The other case is to assume exp[i(wt-kx)] dependence. Then, the imaginary part of the refractive index must me negative.
The difference lies in conventions. Historically, when the wave nature of the light was not known the conventions were different in electrotechnics and optics. As an optician I use (n + ik) convention. Also this is used in the clasical book of Edward D. Palik “Handbook of optical constants”. To see Wiki:
http://en.wikipedia.org/wiki/Refractive_index#Complex_index_of_refraction_and_absorption
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