An amusement park is a collection of rides and entertainment attractions. A theme park is an amusement park where the architecture, rides and entertainment is built around some central theme. A classic example of a theme park is Disneyland, where all the rides and entertainment are based on Disney movies, cartoons and characters.

Theme park and amusement park mean the same thing. Outing is acceptable. You can also say "to spend time/to be in the fresh air/great outdoors".

I have to say, that is a funny question. I can't imagine why this concerns you. A Theme Park can be an Amusement Park. The words themselves describe what the park is. Theme is theme based. Amusement is fun, theme or no theme.