One of the significant differences between a token and a coin, is that coins can fork. Tokens are committed to using the code at a specified address on the blockchain. This code is a permanent contract with all of the benefits that it implies. But a coin is really just values written to an address and recorded in a block. That block is recognised as valid if more than half of the network accepts it.
The network of nodes accepts blocks by running a program that applies a series of rules and calculations. If the program gets updated so that the rules change, then it will accept only blocks that meet the new rules. Once it accepts the block, it will transmit its acceptance as the next block in the chain. But for that block based on new rules to be accepted by more than 50% of the nodes, all of these other nodes must be using a program that is also updated to accept the new rules.
Because of this, there is always a transition date or block at which point the updated software will begin applying the new rules. In Proof-of-Work blockchains, it is the miners that create the blocks, and it is the miners that determine what new rules and calculations will be accepted. But in some cases, agreement can't be reached, but some advocates still want a coin based on the new rules. To resolve this issue, they create a hard fork.
This hard fork continues to use the old blockchain up to a particular block, and then writes new blocks to a new fork in the blockchain after that block. So long as there are enough nodes accepting the hard fork to make a functional network, this can succeed.
And it is not always the minority that wants change. Sometimes, the majority want the change, and only a minority want to reject it. In this case, to keep the old coin going after the majority introduce new code into the program that runs nodes, they need to hard fork the blockchain to create a branch that continues on as normal. But then there is the question, "Who keeps the original coin name?"
The majority changing the code will claim that the name should come with the majority, and that it is the true coin because they are obeying the original intention or roadmap of the project. But the minority, staying with the original code, will also feel like they have the right to the original name because it represents that same code that it always has.
This is what happened with Bitcoin Cash. The original bitcoin code was updated to include some segregated witness functionality, and the change was adopted by the majority of miners. This changed code retained the name Bitcoin. But those who rejected the change continued using the old code and accepting blocks added to the blockchain with the old program. But they had to choose a new name and went with Bitcoin Cash.
But as of the 15th of May 2018, the original bitcoin is no more. Bitcoin Cash has changed the code to increase block size to 32MB as well as use Op codes. At this stage it appears unlikely that a fork using the old code will not exist. This is best described as a soft fork. If anyone has news that explains why Cointelegraph and others called it a hard fork, please let us know in a comment.
There are no rules stating who gets to keep the old name. Whether it is the majority or the minority; or whether it is the old code or the new code. This makes it hard for users to know which is the 'true' coin. And many would argue that it makes little difference because whatever you owned before the hard fork, you then own in both forks. The only choice you have to make is which blocks you'll accept when mining.
The other aspect of hard forks that the market is still coming to grips with, is whether it is a case of 'the many-headed hydra' that just gets stronger with two heads every time you lop one off. Or is it a 'divide and conquer' situation where too many forks makes the coin less valuable. So far, it seems to be the case that your portfolio after a hard fork is worth more than it was before. But because market fluctuations are hard to predict, and even harder to assign causes to, this may still be coincidence.