The TV show episode "Fire and Blood" did not differ much from the book. The birth scene was not shown. I recall the the post-birth dialogue was similar to the book as well.
Here's the relevant excerpt from the book (p. 756-757 in the US mass market paperback):
"Tell me how my child died."
"He never lived, my princess. The women say . . ." He faltered, and Dany saw how the flesh hung loose on him, and the way he limped when he moved.
"Tell me. Tell me what the women say."
He turned his face away. His eyes were haunted. "They say the child was . . ."
She waited, but Ser Jorah could not say it. His face grew dark with shame. He looked half a corpse himself.
"Monstrous," Mirri Maz Duur finished for him. The knight was a powerful man, yet Dany understood in that moment that the maegi was was stronger, and crueler, and infinitely more dangerous. "Twisted. I drew him forth myself. He was scaled like a lizard, blind, with the stub of a tail and small leather wings like the wings of a bat. When I touched him, the flesh sloughed off the bone, and inside he was full of graveworms and the stink of corruption. He had been dead for years."
Darkness, Dany thought. The terrible darkness sweeping up behind to devour her. If she looked back she was lost. "My son was alive and strong when Ser Jorah carried me into this tent," she said. "I could feel him kicking, fighting to be born."
"That may be as it may be," answered Mirri Maz Duur, "yet the creature that came forth from your womb was as I said. Death was in that tent, Khaleesi."
"Only shadows," Ser Jorah husked, but Dany could hear the doubt in his voice. "I saw, maegi. I saw you, alone, dancing with the shadows."
"The grave casts long shadows, Iron Lord," Mirri said. "Long and dark, and in the end no light can hold them back."
The TV show episode did not show the birth and the scene based on this excerpt contained essentially the same dialogue.
Since there is no birth scene depicted in the book or the film, the reader is left with the report of Mirri Maz Duur, who has proven to be untrustworthy in some matters, and rumors from others based on what Dany's servants saw. It is possible that Mirri created these rumors herself and killed the child in order to prevent the prophecy about the child from coming true. It is also possible that Mirri knew she would be dead soon so she had nothing to lose and no reason to lie to Dany. The author left it up to the reader to decide on the accuracy of these accounts.
Addendum: There is precedent for a stillborn Targaryen baby with dragon features. From the short story The Princess and the Queen, Rhaenyra Targaryen gave birth to a stillborn child:
When the babe at last came forth, she proved indeed a monster: a stillborn girl, twisted and malformed, with a hole in her chest where her heart should have been and a stubby, scaled tail. The dead girl had been named Visenya.