MySql version and MySql Library version Does the version of MySql Library have the same impact as the version of MySql server when it comes to other software requirements?

Example: I run Magento 1.9.3, which specifies MySQL 5.6 as a minimum requirement.
If my web server installation is running MySql Library of an older version (5.1.73), what problems will this cause, if any?

I can't seem to find any definitive answer out there regarding this detail?
(A pseudo-answer, since it has been several weeks.)

Libraries tend to work across a wide range of server versions.  I cannot address the specifics here, but suspect there would not be an issue.