I played World of Goo by 2D Boy and Cut the Rope by ZeptoLab. Both are physics-based puzzle games, but World of Goo has a grungy post-apocalyptic theme while Cut The Rope has a more whimsical candy-and-crafts theme centered around different types of boxes (cardboard, etc).
The fact that I didn’t initially think of these games as being in the same genre speaks to the effectiveness of theme in differentiating them. Everything about World of Goo serves to immerse the player in its theme, from the darkly cartoony visuals to the a-little-gross-but-silly sound effects to the ominous soundtrack, while Cut the Rope employs bright colors, cheerful music, and inoffensive sound effects for a theme that is clearly present but less in-your-face. I find it interesting that some of the sound effects used by the two games are actually very similar — the noises made by Om Nom and the goo balls — but the game’s atmosphere changes the way those sounds come across, with Om Nom’s noises coming across as cute while the goo balls’ noises are… still cute, but with a grotesque undertone.
Another thing that stood out to me as a difference between these two games is that their thematic difference is accentuated by a difference in level design. Levels in World of Goo are structured so that they appear to take place within a larger world, in a dangerous and sludge-filled (though still cartoony and whimsical) post-apocalyptic landscape which the player must solve puzzles in order to navigate. The fact that the level select screen is designed like a map emphasizes this. In contrast, levels in Cut The Rope are each contained to a single box (represented visually as a physical box) with puzzle elements arranged within that box that don’t seem to serve any particular in-universe function outside of the challenge they present to the player. The level select screen is also just a series of boxes that open into menus. The game therefore feels much more abstract, like the theme is only there to decorate the puzzles, whereas World of Goo conveys the feeling that the world and theme are its core and the puzzle mechanics are merely the player’s way of interacting with that world.