FILTER vs CASE in Postgres

Lukas Eder hits on an interesting data point:

I’ve found an interesting question on Twitter, recently. Is there any performance impact of using FILTER in SQL (PostgreSQL, specifically), or is it just syntax sugar for a CASE expression in an aggregate function?

Click through for the answer and your daily reminder that SQL variants aren’t pure fourth generation languages—if they were, the optimizer would take all possible constructs of a given desired operation and generate the same execution plan for all of them.