Starling still works that way, and the classic API certainly hasn’t changed. Starling’s interface mirrors the classic API closely and as much as possible. But some things are different.
Instead of BitmapData there’s Texture, and they are very different Textures live on the GPU which restricts what you can do with them, compared to BitmapData. Textures are used in an Image to be drawn, while BitmapData is used in a Bitmap.
The Image class is equivalent to the flash.display.Bitmap class - each contains the image data and lets you move, scale, rotate and modify other aspects of how it is drawn. Each inherits from DisplayObject in each API, the base class for things being drawn. Each can be added to Sprite containers, which is the concrete implementation of the abstract DisplayObjectContainer class. This works the same in both APIs.