Almost always, a tessellation covers a flat 2 dimensional plane, completely, without overlaps. That's a little arbitrary. Why not broaden that definition to include non-flat surfaces, like the cylinder shape of a coffee can or the conical shape of a lampshade? How about the surface of a ball? How about the flat donut shape of a CD or DVD?
Have you ever seen a video game, or a space movie made after the year 2000? Those computer graphics are almost always a wire frame model covered with triangles. We call that "tessellation" too, just like the art we do on this website. Over the wire frame is a surface we call "skin".Wire frame tessellations and painting skins are both full time jobs in Hollywood and Silicon Valley and Pixar™.
Below are some nonflat surfaces I've tessellated. Some are balls; most are dodecahedrons. A dodecahedron is a ball-like shape made from 12 pentagons.