So does every cryptocurrency including bitcoin and altcoins have their own different type of blockchain?
Yes and No.
Yes, because every cryptocurrency executes its transaction with the help of blockchain.
No, because in crypto we have coin and token.
Coins are cryptocurrencies that have their own blockchain. An example is BTC, ETH, BNB, LTC, TRON, SOL, etc.
Token are cryptocurrencies that rely on another cryptocurrency blockchain it executes their transaction. An example is USDT, CAKE, UNI, etc.
I understand that you know the difference between coins and tokens, but the answer is only no because some cryptocurrencies do not have their own different blockchain just like you later said. We can not daily yes because each crypto currency execute its own transaction, tokens still rely on the blockchain of the coin which was used to make the token to be existing, the token even rely on the coin as fee.