You never apply textures directly to an object, there is no such thing as directly assigning an image to a mesh.
"Visible textures" are always applied to a material. This may seem incorrect at first, because some applications hide this fact from you by automatically creating a material in the background for said texture, or some times an object already as a blank material applied to it, and the texture is assigned to it instead, but generally speaking you can't just put a texture on an object.
Exception being that in Blender you have Object Textures (like Clouds you found) which are used by modifiers, particle systems and other object level data. These can't really be made directly visible, or used in a material per-se. They can only be made visible indirectly through their influence in geometry, like say in a Displace Modifier.
UVs are one of the several type of Texture Coordinates, obtained through the process of Unwrapping a mesh. They are a completely different type of data and are used to map any texture (material or otherwise) over a mesh, so the application knows which part goes where.
There are several types of coordinates that can be used for different requirements, some of them don't require unwrapping.