In summary, the main differences between volume and object store are:

File Access
Volume or Block storage can be seen as what we know as a partition of a harddrive (or a whole hard drive), containing a lot of files in one continuous block. Files are accessed with traditional file access methods. In the Object Storage, files may be spread over several hard-drives. An object is accessed using a http based interface.

Distribution
Object Storage is a per-file based storage system which stores each file at several locations — you won’t know where exactly the individual files are stored, they may even not all be on the same harddrive. In contrast, Volume Storage is one block of storage which contains several files, located at one location.