Are tennis shoes really any different than sneakers?

Yes they are. For a long time, the term, 'tennis shoe', was used as a generic term applied to any athletic shoe worn for casual purposes. Actual tennis shoes have several features designed for playing the sport.

Many of them have tread that covers the toe area, because so many players will play while on their toes. On the sole, they have pivot points on the balls of the feet to protect from wear and tear in that area. Tennis shoes are also designed to prevent the foot from sliding around inside, since there is a lot of lateral, stop-and-go and change of direction movement.

Shoes designed for clay courts are designed in such a way that they keep the clay out of the shoe and some have cleat-like knobs to limit sliding while playing on clay surfaces.