Heileen 2 continues the story of (naturally) Heileen, a girl who travels to the New World with her uncle for complicated plot reasons. Heileen 2 finds her shipwrecked on an island having various adventures.

There's a bit of a tone change between Heileen 1 and Heileen 2, which can perhaps best be summed up like this:
In the first Heileen game, she talks to her cat.
In the second Heileen game, her cat talks to her.