It should be also mentioned that the "Generated" texture coordinates uses the texture space box that can be moved or scaled in "Object" mode under "Object" => "Transform" => "Move Texture Space" or ""Scale Texture Space"
The bigger box in the image above is the "Texture Space Box". It can be made visible in the "Viewport Display" panel of the "Properties Editor" by checking "Texture Space". The location and scaling of that box can also be adjusted precisely and for each axis individually in the "Texture Space" panel in the "Object Data" tab of the "Properties Editor". You can reset the texture space box to the default by checking "Auto Texture Space" in the panel mentioned last.
The "Object" texture coodinates use the object's "Bounding Box" (smaller box in the image above).
"Texture Space Box" and "Bounding Box" have identical dimensions and position for a newly created object or the default cube.
