PostgreSQL (colloquially referred to as Postgres) is an open source object-relational database system with over three decades of active development. Over the years, it has consistently established iteself as the most reliable and feature-rich database, truimphing over popular databases like MySQL.
MySQL has historically held a reputation for being an extremely fast database for read-heavy workloads. This is often at the cost of concurrency when mixed with write operations. It established itself early on as the fastest database in the world but that advantage has been mostly erased with newer versions of Postgres.
Postgres, on the other hand, rose to fame because of its ability to handle concurrency better than MySQL and could handle write operations much more efficiency. This write performance was mostly at the cost of read performance, but they managed to patch it up in newer versions.
MySQL is still a very fast database, especially at handling reads, but it's a lot more efficient if you rely on the MyISAM engine. In order add transactions, key constraints and other important features, you'd have to use InnoDB.
That said, when choosing between MySQL and Postgres, performance shouldn't be a factor that lets you settle on one database over the other. Postgres does have other advantages over MySQL, but both databases perform more or less the same if managed correctly for smaller applications.
Microsoft SQL Server is a database analysis and management platform that's normally used for ecommerce purposes. Postgres does come with advantages when it comes to support for files like JSON and CS, though. Microsoft SQL Server is also vendor locked. It can only be run on Microsoft systems while Postgre can run on any operating system.