A DApp is a decentralized Application. This is usually a set made of:
A specific smart contract is deployed on one or several chains. It depends what the author decided to do.
Regarding your frontend, you could implement it so it can interact with your smart contract on all the chains you support.
So if your smart contract is deployed on mainnet + testnet for instance, you could write your frontend to support both.
So a given DApp may or may not have it's own blockchain. It depends.
For example, there's the Ethereum mainnet, which is public, and anyone can have their dApp interact with it. In this case the dApp doesn't have it's own blockchain.
However, anyone can fork or run their own copy of Ethereum, which in this case, it's a separately owned blockchain instance so it'll have it's down data and blocks not pegged to the public mainnet blockchain.