CREATE INDEX vs ALTER TABLE ADD INDEX - MySQLism, or SQL Standard?
I don't think that the SQL standard defines how to create indexes at all.

A quote from this Wikipedia page:


  Standardization
  
  There is no standard about creating indexes because the ISO SQL
  Standard does not cover physical aspects. Indexes are one of the
  physical parts of database conception among others like storage
  (tablespace or filegroups). RDBMS vendors all give a CREATE INDEX
  syntax with some specific options which depends on functionalities
  they provide to customers.


The Postgres manual seems to support this here:


  There are no provisions for indexes in the SQL standard.


More evidence under this related question on SO.