Regression testing is a type of testing that is performed after a software system has been changed or modified to verify that the changes have not introduced any new defects or adversely affected the existing functionality of the system. Regression testing can be performed when the software system undergoes different types of changes, such as:

Corrective changes: Changes that fix defects or errors in the software system

Adaptive changes: Changes that adapt the software system to new platforms or environments

Perfective changes: Changes that improve the performance or usability of the software system

Preventive changes: Changes that avoid potential problems or issues in the software system

In this case, the software system was re-deployed because the backend database was changed from one vendor to another, which is an example of an adaptive change. Therefore, the test manager decided to perform some functional tests on the re-deployed system to ensure that the change did not affect the functionality of the system. This is an example of regression testing.

The other types of testing mentioned in the question are not relevant for this scenario. For example:

Non-functional testing: This type of testing verifies the non-functional aspects of the software system, such as reliability, performance, security, usability, etc.

Structural testing: This type of testing verifies the internal structure or implementation of the software system, such as code, architecture, design, etc.

Unit testing: This type of testing verifies individual components or units of software in isolation from other components or systems.

You can find more information about regression testing in [A Study Guide to the ISTQB® Foundation Level 2018 Syllabus], Chapter 2, Section 2.4.