As far as I can tell today (June 2011), both gems are the same.
On RubyGems.org sqlite3 and sqlite3-ruby point to the same sqlite3-ruby repository on github.
From the project description on github:
This module allows Ruby programs to interface with the SQLite3 database engine (http://www.sqlite.org). You must have the SQLite engine installed in order to build this module. Note that this module is NOT compatible with SQLite 2.x.
One of the maintainers confirmed the renaming of the gem from sqlite3-ruby
to sqlite3
here:
This announcement is to let you know that the sqlite3-ruby gem is being
renamed to (drum roll please) "sqlite3".
We will maintain backwards compatibility by releasing an empty
"sqlite3-ruby" gem that depends on "sqlite3". The empty sqlite3-ruby
gem will contain a post installation message that will inform people to
make the switch.