jrauman
This answer has some subtleties, so bear with me.
I don't own the old drivers, but from experience, I can confirm that file versions for the old ODBC drivers generally match the SQL Server version information.
See Latest updates and version history for SQL Server - SQL Server | Microsoft Learn.
Given your list, I noticed "13.3.x" doesn't match anything on that doc page, but Microsoft SQL Server Versions List lists 13.3.6300.2 as an alternate version number to 13.0.6300.2 under SQL Server 2016 SP3. I assume that website doesn't have the latest update and that 13.3.7024.30 corresponds to 13.0.7024.30 since everything but the minor version matches up to the latest SQL Server 2016 SP3 update release. Given the above, here's what your versions correlate to:
13.0.1601.5
|
SQL Server 2016 RTM (no updates applied)
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13.3.6300.2
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SQL Server 2016 SP3 RTW/PCU3
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13.3.7024.30
|
SQL Server 2016 SP3 Azure Connect pack + GDR
|
14.0.1000.169
|
SQL Server 2017 RTM (no updates applied)
|
14.0.3460.9
|
SQL Server 2017 CU31 + GDR
|
If all your ODBC driver installs are in the scope of a SQL Server install, all you need to do to update the drivers is apply the relevant SQL Server update.
If you have driver installs outside of the scope of a SQL Server install that you can't migrate to the latest 17/18 versions, you'll need to manually extract and install the appropriate msodbcsql.msi from the latest SQL Server updates as I described in my previous comment.
There is an additional scenario I'd like to describe for SQL Server installs. 13.x and 14.x are all valid file versions for "ODBC Driver 13 for SQL Server". "ODBC Driver 13 for SQL Server" was shipped with both SQL Server 2016 and SQL Server 2017. Within SQL Server 2016, "ODBC Driver 13 for SQL Server" is versioned 13.x. Within SQL Server 2017, "ODBC Driver 13 for SQL Server" is versioned 14.x. When updates are made to either of SQL Server 2016 or SQL Server 2017, you will get a newer 13.x or a newer 14.x. Both of which can be considered the "latest version" within their line. However, only one of them can be installed on a system at a time, unlike the other MS ODBC driver major versions. And a version 14.x ODBC driver will upgrade and replace a version 13.x ODBC driver. Given versioning semantics, I would assume any version 14.x driver will upgrade/replace even a newer 13.x driver. If a 14.x ODBC driver ever replaced a 13.x ODBC driver on a SQL Server 2016 system (tools like SSMS also install a version of the ODBC driver), it would functionally work fine, but a subsequent SQL Server 2016 update would not (I assume) patch the 14.x ODBC driver since the 14.x driver would be a newer version. Solutions for this scenario would be to manually update the 14.x ODBC driver or uninstall the 14.x driver and install the 13.x driver so that future SQL Server 2016 updates will patch it.
Regards,
David