So you do have a physical hard drive and should have an additional SSD, right? Well, in My Computer, how many "drives" do you have? There most certainly will be a C: drive. What is its size (capacity). You may have an optical drive for DVD's which will have its own letter name, but not be available for storage, and you will not be able to read it either unless there is a disk in it. Any other "drives"? If there is a second drive that you can read and write, probably you have both a SSD and a HDD. What is the size of that unit?
One way an SSD can be installed is in a special slot in the mobo. This type is called an M2 type SSD. It works exactly the same as the little box you are searching for, but it looks like a small circuit board...