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Disneyland Resort in Anaheim contains two theme parks (they're located next to each other on the same property): Disneyland Park and California Adventure, plus a couple of hotels and an unticketed shopping area called Downtown Disney. Disneyland Park is the classic, iconic Disneyland, while California Adventure is a newer California-themed area.
When you buy admission tickets, you can buy single park tickets, which grant admission to one park per day (if you buy a 2-day ticket, you can visit a different park on different days or the same park both days) or pay more for "park hopper" tickets, which allow you to go between parks on the same day.
Tom Sawyer Island (also other things you've circled like the Haunted Mansion and the Pirates of the Carribean ride) is an attraction inside of Disneyland Park. Rides and park attractionsβexcluding things like parking fees, special tours, food and drinks, souvenirs, etc...βdo not require additional tickets and are included with your admission ticket.
The Disneyland website has a list of attractions, which you can filter by park and type. There are also many blogs and web sites that go into (too much) detail on planning Disney trips. This page from Mouse Hacking has a good overview of the basics, including the details of the FastPass and MaxPass systems, with links to many more resources.