Filtering and Fourier Transforming, does the order matter?
There may be some slight differences due to the band-pass filtering of FFT results in the frequency domain being a circular convolution (with some wrap-around artifacts) rather than a pure linear convolution.

If you filter first, starting in time before your FFT window, any windowing artifacts from any out-of-band spectrum will be reduced before leaking into the FFT filter's pass-band.  Or alternatively, you could zero-pad the FFT window by the length of your filter's impulse response.