The hive was designed to appeal to a community comfortable with SQL. Its philosophy was that we don't need yet another scripting language. Hive supports map and reduces transform scripts in the language of the user's choice (which can be embedded within SQL clauses). It is widely used in Facebook by analysts comfortable with SQL as well as by data miners programming in Python. SQL compatibility efforts in Pig have been abandoned AFAIK - so the difference between the two projects is very clear.
Supporting SQL syntax also means that it's possible to integrate with existing BI tools like Microstrategy. Hive has an ODBC/JDBC driver (that's a work in progress) that should allow this to happen in the near future. It's also beginning to add support for indexes which should allow support for drill-down queries common in such environments.
Finally--this is not pertinent to the question directly--Hive is a framework for performing analytic queries. While its dominant use is to query flat files, there's no reason why it cannot query other stores. Currently, Hive can be used to query data stored in Hbase (which is a key-value store like those found in the guts of most RDBMSes), and the HadoopDB project has used Hive to query a federated RDBMS tier
