This sense is the fruit. In British English, pawpaw is often just another name for papaya: a large tropical fruit, yellow-green on the outside, orange or yellow inside, soft enough to eat with a spoon, often with lime. That is the tidy dictionary picture, and it is how many UK speakers use the word. Though actually American English is messier. In the United States, pawpaw usually means a different fruit, from a different tree, that grows in the woods of the eastern US. It is yellow-green too when ripe, and people say it tastes a little like banana and mango mixed, but it is not the supermarket papaya. So a British recipe that says pawpaw almost certainly wants papaya. An American nature story about pawpaws in autumn is talking about the other fruit. Learners are not being silly if the two uses collide; the language really did split.

木瓜（英式多半＝papaya；美式另指北美「巴婆果」）