The 'Y' is used for imagination. In reality there is no real split.
Each node stores its own copy of the blockchain. When a hard fork occurs there are basically 2 versions of the blockchain spread between nodes.
Both versions have the same data until block X. The representation with an 'Y' seems to be the most popular one. But from block X those are 2 completely independent networks.
Its wrong to say that a hard fork occurs when there are 2 versions of the blockchain. That situations also occurs in a soft fork. The actual difference between a hard fork and a soft fork is determined by the ability of the nodes on the main chain to validate blocks that are produced in accordance with the consensus rule of the fork.
The Y is is basically what you see if you draw a graph of the split.