Search for a files that matches another file name in another folder

I have some files in a folder, which are named ***_code_c**** (where * represents any letter or number). I have another folder that have many files, folders and subfolders inside it. What I want to do is to look for and copy to another location any files that matches the names of these files like ***_code_c**** but with only two letters different like this ***_mode_m**** and ***_kode_c**** and any of the files that matches this criteria will be copied to a specific folders where the ones having the mode instead of code will be placed in a folder and the ones having the kode instead of code will be placed in another folder. If anyone could please advise how this can be done. Thanks

Example to clarify what needs to be done:

FolderA has some files in it lets say ABC_code_c001, CDE_code_c002, FGH_code_c003 ...

Another FolderB has many files, folders and subfolders inside it.

for every file in FolderA there is a corresponding two files in FolderB which are named exactly the same except for the middle part. For example the corresponding two files of ABC_code_c001 are ABC_kode_c001 and ABC_mode_m001, while the corresponding files of FGH_code_c003 will be FGH_kode_c003 and FGH_mode_m003 and so on

So, what I want to do is to take every file in FolderA and search for the two corresponding files in FolderB then copy each of these two files in two other folders lets say FolderC and FolderD(one in each).

Note that the names I'm using is not the exact names I listed in the example, but it has the same idea where the difference between its name and the two other names will be one letter in the middle from c to k and m.