During the proof of work process, a miner receive a block to mine.

He mines it, whether the miner is rewarded or not, this block is added to his own chain.
So at once, his has a chain which is different from the main chain.
At this time could we say there are as many btc chains as there are miners ?

Next, is my understanding correct ?
The miner looses against miners, the block becomes orphan, and the miner's chain reverts back to the main chain (somehow) and he waits for the next block to be mined.