If you pay to enter Disney, with that same pass can you enter Disney adventure or do you have to pay separately?

No. You can buy a "Park Hopper" ticket to enter the two parks.

Edgar if you want to live a good experience I recommend you buy one day for Disneyland and another day for California adventure the time is not enough to enjoy the two parks in one day. And for your question Carol and Vanessa are right

Apart if you do not buy park hopper