Databases vs Schemas
PostgreSQL and MySQL differ on databases vs schemas terminology. While creating constraints such as foreign key, MySQL lets anyone reference tables across databases (without explicitally using schema). OTOH, PostgreSQL doesn’t have any way to maintain cross database references (as of PostgreSQL 8.2). So, although MySQL’s implimentation is non-standard (and incorrect) it is more functional in this case.
MySQL aliases schema with database behind the scenes, such that create schema and create database behave identically. It can be said that MySQL therefore has implemented cross-table functionality, skipped schema functionality entirely and provided similar functionality into their implementation of a database. In summary, Postgres fully supports schemas, but lacks some functionality MySQL has with databases, while MySQL doesn’t even attempt to support true schemas.