No, we don't have any online documents talking about the difference between TA_USER and TA_SYSTEM. We have comments in every programming language that supports comments on constants (which, ironically Xojo is one of the only languages that doesn't allow that).
The best reference is the TurboActivate.h file in the "API\C" folder.
The only real difference between TA_USER and TA_SYSTEM is where the files are stored: either on a per-user basis (thus, no TA_E_PERMISSION error will ever be returned) or on a system-basis (i.e. all users will have access to the data).
As mentioned in TurboActivate.h when you use TA_SYSTEM on either TA_UseTrial() or TA_CheckAndSavePKey() you'll need admin permission the first time you call the function with TA_SYSTEM. However, after that, you don't need admin permission. The first time you call those functions with TA_SYSTEM, TurboActivate sets everything up so all users have access to the data.