Six images arranged as a box
Skyboxes & cube maps
A cube map is a texture you index with a direction rather than a coordinate pair. Hand it a vector, it works out which of six faces that vector points at and samples there. Use the direction you are looking and you have a skybox; use the direction light bounces off a surface and you have a reflection. Same texture, same lookup, two different vectors.
The yellow marker is the face and texel the centre of the view lands on. Rotate and watch it cross a face boundary — that is the only moment the hardware changes which image it is reading.
The data is identical — six images on the faces of a notional cube. What differs is what you do with it.
A skybox is drawn as background. It is sampled with the view direction, ignores the depth buffer, and never moves with the camera's position — only its orientation — which is what makes it read as infinitely far away. Walk towards a mountain in a skybox and it never gets closer.
A cube map used for reflection is sampled per pixel of an object with the reflected view vector. It can be captured live from the object's own position each frame, which is why a reflective car can show the scene changing around it while a skybox cannot.