If we are talking about a production database, the most reliable and time-tested algorithm, perhaps-as follows:
1. The changes to the database are issued in the form of the so-called migrations. Engines to implement SQL migrations-complete. In the simplest case, migration is simply a set of DDL/DML issued in the form of, for example, SQL script.
2. Migration is stored in a VCS. Anyone seen what changes are made.
3. In production migrations are applied automatically under control of the DBA or the DBA. The DBA role can perform any responsible person if you do not have a dedicated person.
4. (bonus) the database Schema in production after each application migration is unloaded in the same VCS as a separate script contains only DDL and reference data (example: data for filling the table of car brands, the data for filling the table of countries, etc.). It is convenient for rapid deployment of development environments in sync with the current production database schema.
Something like that.