Call ActiveRecord::ConnectionAdapters::SchemaStatements#tables. This method is undocumented in the MySQL adapter, but is documented in the PostgreSQL adapter. SQLite/SQLite3 also has the method implemented, but undocumented.
>> ActiveRecord::Base.connection.tables
=> ["accounts", "assets", ...]
See activerecord/lib/active_record/connection_adapters/abstract/schema_statements.rb:21, as well as the implementations here:
activerecord/lib/active_record/connection_adapters/mysql_adapter.rb:412activerecord/lib/active_record/connection_adapters/postgresql_adapter.rb:615activerecord/lib/active_record/connection_adapters/sqlite_adapter.rb:176