If you look at the kernels you'd see they are both approximations of Gaussian Kernel.
So basically their subtraction is the Difference of Gaussian (DoG) kernel.
Analysis of the Kernels
As one could see, both kernels are symmetric.
If we analyze their singular values, to check for separability, we can see that the 1st kernel is separable while the 2nd is not.
Yet, still the 1st singular value of the 2nd kernel is more than an order of magnitude bigger, so we can analyze their basis vectors to move into 1D analysis.
Looking at their 1D Row / Column filters:
We can see they are almost equivalent except Kernel B has a wider support.
Wider support means lower bandwidth in the context of LPF filters, as their sum is 1.
Hence their subtraction creates a Band Pass Filter:
Since the 2 variants are multiplication by $ -1 $ of each other, they are both the same filter in the magnitude. Since they are applied in an LSI manner, it means also the result will have a negative value of one to each other.
The result isn't surprising as indeed the DoG filter is a BPF filter.
The full code is available on my StackExchange Signal Processing Q86094 GitHub Repository (Look at the