In this context, I'd say the two meanings were pretty much identical since they are both referring to the current action (of the person asking for the toy), and not their habitual, ongoing action.
And I'd say that goes not only for the literal meaning, but also for any suggestion that the owner of the room (in which the toy was found) feels the request for the toy is unwanted. To just what extent that aspect was conveyed would be more down to the tone, not to mention body language including facial expression. The broader context would be important too. Consider the following three scenarios:
A kid has left a toy lying on the floor of his parents' bedroom. He finds it, takes it to his mom and asks "I found this toy in your room, can I have it?" Mom nods, but puzzled asks, "Why are you asking?"
A robber has broken into a house, tied up the family, and has packed everything they owned into a truck. Just as he is leaving, he spots a toy on the floor of one of the kids rooms. He grabs it and begins to leave, but at the last minute turns to the kid and says, "I found this toy in your room, can I have it?" The kid glares at the robber, shrugs and in a resigned tone says, "Why are you asking?".
One kid had been unable to find a particular toy for weeks. He was sure his brother had stolen it but he could never prove it. One day, he finds the usually-locked door to his brother's room lying wide open, and there in the middle of the floor is his toy! He picks it up, runs to his brother, and says triumphantly, "I found this toy in your room! Can I have it?" The brother starts sweating and looking furtive, and replies, "W'w'w'why are y'y'you asking? [gulp]"