Just read some articles about ICO instead hard-fork. But its not enough info
The way I understood it (and I may be mistaken)
When a change to the block chain is needed/wanted, developers do a hardfork.
Why? Because the chain resides in many places and cannot be changed simultaneously and instantly.
How? By making a full copy of the original, then applying the change(s) to the new one.
There are times when the whole community is in agreement (ideal situation) and the fork will just abandon the old and continue with the new/updated version.
IF there is division and both have enough support then both coins from the fork will continue. Usually, owners of the original coin will also receive a 1:1 qty of the new coin.
Hope this helps a bit.
I think you are mostly right. Examples of hard fork are 2 eth forks and 1 bitcoin fork (a long time ago with no split). Generally, when the chain splits in 2 it is a bad situation, because assets split as well and that results in both versions having price drops in comparison with the original version.
Thre is also a soft work way to make changes (some upgrades) on the original chain, which is less risky. Bitcoin segwit was a soft fork, I guess.