I am confused.. is my SSMS 16.5.3 or 13.0.16106 or is my installation
corrupted or incomplete?
The current version of SSMS is
16.5.3 with a build number of
13.0.16106.4. This means you have the current version already installed.
I had SSMS version 13 on my Win 8.1 64bits machine
You no longer have the previous version of SSMS installed on your system. The previous versions of SSMS was not 13, but were preview builds of 16.3, which was released in August 2016. The major version before 16.3 would be version 12 which was released with MSSQL 2014 which was before the SSMS was seperated from the MSSQL Server release schedule.
There were of course, multiple interim releases between 16.3 and 16.5, I just selected the first stable version released since June 2015.
Version 16.3 of SSMS was released around the time MSSQL Server 2016 SP1 was released.
[Insert Month Here] Preview was released during/after MSSQL Server 2016 was released
Version 12 of SSMS was released with MSSQL Server 2014
In June 2015, Microsoft announced their intention to release future
versions of SSMS independently of SQL Server database engine releases.
SQL Server Management Studio
SQL Server Management Studio - Changelog (SSMS)