Oh I wish I could down vote some answers and up vote others with an account.
The one with the most votes, as of this writing, doesn't even explain anything about the differences.
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.
This explained a large portion of it; but you argued about the meta data. The following is from what I have been reading these last two days, and since this hasn't been resolved, I will post.
Object storage has no sense of folders, or any kind of organization structure which makes it easy for a human to organize. File Storage, of course, does have all those folders that make it so easy for a human to organize and shuffle through...In a server environment with the number of files in a scale that is astronomical, folders are just a waste of space and time.
Databases you say? Well he's not talking about the Object storage itself, he is saying your http service (php, webmail, etc) has the unique ID in its database to reference a file that may have a human recognizable name.
Metadata, well where is this file stored you say? That's what the metadata is for. You single file is split up into a bunch of small pieces and spread out of geographic location, servers, and hard drives. These small pieces also contain more data, they contain parity information for the other pieces of data, or maybe even outright duplication.
The metadata is used to locate every piece of data for that file over different geographic locations, data centres, servers and hard drives as well as being used to restore any destroyed pieces from hardware failure. It does this automatically. It will even fluidly move these pieces around to have a better spread. It will even recreate a piece that is gone and store it on a new good hard drive.
This maybe a simple explanation; but I think it might help you better understand. I believe file storage can do the same thing with the metadata; but file storage is storage that you can organize as a human (folders, hierarchy and such) whereas object storage has no hierarchy, no folders, just a flat storage container.