All bitcoins solve the same problem but with increasing levels of difficulty , is at correct?
Bitcoins don't solve anything. Bitcoins are an abstraction that we humans use to make discussion of value easier. In reality there is nothing that can be pointed to and say "that's a bitcoin". Bitcoins are simply the sum total of the "value" fields of all unspent outputs associated with an address.
All miners solve a SHA-256 hash of the block header looking for a hash that has a value lower than a target difficulty. When they find that hash, they publish the block. In the block is a transaction with no inputs and outputs assigning block subsidy and transaction fees to the miner(s).
If I mine a bitcoin today that barely solves the problem, I should immediately put it in a block and take ownship. But if I mine a bitcoin that solves the problem by a wide margin, I can sit on it because even when the difficulty goes up my coin will still be valid. Is that correct?
Another way to put it is I could mine a coin that would have been a slid bitcoin 6 months ago, but because the bar has been raised, it is not a bit coin today. Today it is worthless.
No. Hopefully my previous post, and previous comment in this post, have clarified this.