Yes, in the Tangram game there are four levels: Easy, Medium, Hard, and Harder. Each level corresponds to a color in the game: easy = yellow, medium = orange, hard = red, and harder = purple.
Junior mode is made up of about a dozen puzzles, some of which use only a couple of puzzle pieces. The game gives the player many visual and audio cues to assist in completing the puzzles. Junior mode puzzles do not use all of the pieces.
Treasure mode features a large map that the player can use to select different puzzles. Treasure mode includes levels Easy, Medium, Hard, and Harder. Every puzzle in Treasure mode uses all of the pieces.
Here is our PDF guide to the Osmo Tangram app: