This is just because C# is case-sensitive, and correct name of the type is
SQLiteConnection
:
http://www.devart.com/dotconnect/sqlite/docs/Devart.Data.SQLite~Devart.Data.SQLite.SQLiteConnection.html[
^].
By the way, the use of "using" clause is optional and does not really relate to the use of some assembly, which is defined by referencing it. It's just about the way you can name assembly-level types, no matter in what assembly; it equally apply to the same assembly, for example. The "using" clause just happens to shorten some names in use.
[EDIT]
Actually, all credit should go to PIEBALDconsult, who wrote nearly the same in his comment to the question; I just noticed that only after I already posted this answer.
—SA