In SQL server during Log Shippping which portion (active\Inactive) of the Log file (.ldf) backup is taken and further restored in SQL Server
I have difficulties understanding your question. Perhaps you can clarify or re-prase? Anyhow:

A regular log backup will clear the contents of the ldf file (a bit simplified). Using COPY_ONLY for the log backup will not clear the contents.

The .tuf file is not related to above. When you restore a log backup, you can specify that you can restore further backup, but still be able to SELECT in the database. This is the STANDBY option. SQL Server need to keep track of some things on this scenario, for the next restore, and this is the .tuf file.