It is hard to compare these two things, I know at first glance they look similar because SQL is an interface for applications in both products, but the main difference is that HAF is a framework to build applications and HiveSQL is a service that responds to SQL queries. HAF is strongly concentrated on applications, it drives them by telling them which block shall they process in the next step, gives them a place to save their own SQL tables, and roll back changes in case of micro-fork occurrence. HiveSQL allows only for asking the remote database. HAF is completely free, all its components, includes the PostgreSQL database, have opened code and the community may participate in its development. HiveSQL has closed code. Because HAF allows saving the applications tables in the same database as the blockchain data are, applications are very performant - they have no delays because of asking for external service. HiveSQl is immediately ready to use ( after subscription ), HAF requires to setup somewhere all of its components, but projects similar to Hive Plug and Play may solve this problem.
In general, to reiterate what I wrote at the beginning, it's hard to compare a framework with a service.
RE: What is HAF ?