Does Linux employ any SID equivalent to Windows OS's?
No - but how does that fit in? Are you thinking of the uid?
If you use the same name you have to make sure you have the same uid
So in your Kubuntu check what uid you have - it should be 1000
uid = user id You can find it in Users and Groups, probably on the Advanced tab (it might be called something similar in KDE)
Next all the hidden files and folders in your home have to be removed - create a folder and put them there, there might be some useful info. This is very critical
If you don't you will get a real mess and the uid will probably not be set at 1000 which will lead to problems
Even if it was the KDE edition of Mint this would be the case due to the difference between the DEs
Reinstalling the same system does not have these problems and installing a newer Mint of the same taste (Gnome, KDE, etc) does not have the problem either even if the recommendation is to remove existing hidden files and folders to get a fresh Mint
Or in short - never use the same home and user name
for different systems, that's why you have to take action, but it's quite OK to use the same home with different user names