Does a file system also use block storage?

I'm confused about the actual internal workings of a file system. The question is about file storage vs block storage. From what I understand, the difference is in the level at which we access data: File storage at a file level and block storage at block level. My question is: Does file storage also ultimately divide the file in to chunks and store it again on individual blocks? And so the difference is really in who is responsible for combining these chunks to form the file? In case of block storage this is done by the OS on that block server and in case of file storage it is the OS with help of the file system? Follow up: In case of block storage, how does the OS keep track of the various chunks of the same file without using a file system then?