There are some very fundamental differences between File Storage and Object Storage.
File storage presents itself as a file system hierarchy with directories, sub-directories and files. It is great and works beautifully when the number of files is not very large. It also works well when you know exactly where your files are stored.
Object storage, on the other hand, typically presents itself via. a RESTful API. There is no concept of a file system. Instead, an application would save a object (files + additional metadata) to the object store via. the PUT API and the object storage would save the object somewhere in the system. The object storage platform would give the application a unique key (analogous to a valet ticket) for that object which the application would store in the application database. If an application wanted to fetch that object, all they would need to do is give the key as part of the GET API and the object would be fetched by the object storage.
Hope this is now clear.