Different representations of frequency space of 2D image FFT
The second image you find online as you mentioned is magnitude and the first image must be either real part or the imaginary part (but not both). If you calculate complex value magnitude for each point, i.e. $Mag_{i,j} = R_{i,j}^2 + I_{i,j}^2$ you get something similar to the following image.

I = imread('cameraman.tif');
F = fft2(I);
F_Centered = fftshift(F);
Mag = abs(F);
imshow(Mag);




but taking log10 harnesses the large magnititde of some frequency bins so for visulasation the normalization does not round them to zero.

imshow(log10(Mag),[])




Thus applying the filter on the above image which is only processed for visualization is not correct and inverse FFT of the values would not have much meaning.

To apply your filter you get the fft of the image, F(image) , then you need to make a same size mask image (all 1 and the frequency section you need to be removed must be zero, also remember symmetry feature of Fourier) and then apply do a element wise multiplication of fft values with this mask.

Also, I would suggest to watch this short lecture by Hoff on this subject:

https://youtu.be/02c6ohQV2TA