See above, How to transfer BTC to an offline wallet which is never connected to internet (here don't bother about hard wallets). If yes, then this transaction is off-chain transaction right?
~Rude Boy
See redsn0w's answer first.
You misunderstood what is "off-chain" transaction.
Off-chain transactions are transactions which isn't stored in "Blockchain". When you do an off-chain transaction, the Bitcoins aren't "really" being moved. You are only getting a confirmation receipt from the company. Off-chain transactions are generally bad and it contradicts some of Bitcoin rules:
• You
need to trust the company or person who handle off-chain transaction.
• Off-chain transactions
are reversible.
• Off-chain transactions
promote & focus on centralization.
• Off-chain transactions
don't have public proof(aka ledger).
There maybe more but I think this is more than enough.
If you didn't understand redsn0w's correctly, here is an answer from Stackexchange.
The "blockchain" is a constantly growing database of transaction information which is sent out to all nodes in the Bitcoin network. When you perform a transaction, that transaction is distributed to the network and assuming the transaction is valid, will be included in the next "block." This is where the coins themselves are stored. When you initiate a transaction, all previous transactions to or from that address are scanned and a balance is calculated. If your transaction exceeds this available balance, it will be rejected by the network and will not be included in a block.
It's also important to note that the blockchain technically doesn't store "coins" it stores transaction information. The coins themselves are not discrete things which need storage - when coins are mined the miner's balance is credited via a "generate" transaction which adds to his or her available balance. When coins are sent from A to B, that transaction subtracts from A's balance and adds to B's balance. This is similar to the way that your employer may, via EFT, send "money" to your bank and you can use your debit card to spend that "money" in a store, all without anyone ever seeing a discrete physical dollar bill. Most money in the world today exists merely as transaction histories and balances - Bitcoin is no exception.
Edit: Added few words.