Creating new database

Dear All,

I've been using a single database for many years.
I'd now like to create a new separate database with most of the same
tables, so that I don't have to re-write my code, I'd like to just use a
different Tomcat datasource to access it.

I had imagined this would be as simple as :
1) using createdb, to create a database with a different name, maybe
with a different postgres user assigned to it,
2) using a pg_dump from the original database to import the table creation.

However it doesn't appear to be that simple.

Let's say the old database is called database1, and I've created a new
database2.

When I import the pg_dump into database2, it tells me that the tables
already exist (obviously it's talking about the tables in database1).
But I surely I've created a new database called database2? Why is it
stopping me from creating the same tables in the new database?

Same sort of problem with psql:
If I run 'psql database2' then I see everything from database1 as well.
What am I missing here?

Thanks for your time.

Malcolm Warren