Don’t waste too much time on it. This is just a technicality which can be ignored most of the time.
A material slot is an entry in the material list. It can be empty, i.e. without a name.
A material is an entry in the material list. It always has a name.
It is also possible to have temporary materials without a slot. They appear only in the material drop down menu to be assigned to a slot. They live only as long as the current session. They can’t be assigned to meshes.
When the material list of an object is empty, there is a button “New” below it which will create directly a material with its slot. Or else, you can use the material drop down menu to re-use an existing material (from an other object or without slot).
If you use the button “+” on the right of the list, it creates an empty slot. The widget below the list will then just assign a material to the slot. Just do it so you don’t have to deal with slots any more.
Note however that materials are generally referred to only by their slot number throughout Blender. (I really hope this issue will be addressed in the coming UI overhauls… but I won’t hold my breath.)
Alright, that will be all for today. I still have a lot to say about material management but it’s more related to material users than slots.