The difference between internal and external conflict is that internal conflict is within the being of the character, whereas external conflict is environmental, meaning it takes place outside the character's own being. An example from the story of internal conflict is Moose's dislike of being on Alcatraz Island. An example of external conflict is Moose's need for time with his parents when they have job and family obligations that take them away from him.
Conflict can be tension, struggle, fighting, contention, battle, or strife. If the conflict is psychological (internal), it is in the mind, emotions, or psyche (soul or spirit) of the character. If the conflict is environmental (external), it is against nature, another person, or any other oppositional, antagonistic force.
The first internal conflict Moose acknowledges is his inner mental and psychological conflict about being on Alcatraz Island. He didn't want to be there. He didn't want to be away form his best friend Pete.
I want to be here like I want poison oak. . . But apparently nobody cares, because now I'm Moose Flanagan, Alcatraz Island Boy [. . . ] "with some swell fellows like Al Capone and Machine Gun Kelly."
The second internal conflict is inner mental and psychological conflict because Moose's sister's needs clash with his own needs, and her needs have to take precedence. It is clear Moose loves and is devoted to Natalie, but he knows meeting her special needs (i.e., her need to be in Esther P. Marinoff school) prevents his parents from meeting his particular needs for a stable school life with unbroken association with his friends and activities.
An important external conflict that helps drive the plot is that Moose wants time with his parents for himself. When the story opens, he hasn't seen his dad for "three months." On the very day he hopes to make up for some of that lost time, Moose learns his dad has to work, is "leaving now," his mother is also leaving to do shopping, and he has to watch over Natalie to keep her safe.
The first two examples are internal conflict because they are conflicts within Moose's own thoughts and feelings. He wants things he can't have because there are more important things the family needs, and he has a hard time adjusting his disappoint so he doesn't feel let down, angry, or resentful.
"I didn't really mean what I said about it not being fair. . . I didn't. You know I didn't."
The third example is external conflict because it is conflict with two other people—Moose's parents. He wants something from them that they can't give because of their own needs that they have to contend with, such as jobs, Natalie's needs, and the family's needs.