1, Testnet is an application for development which mimics the main net, minus the financial or security risks.
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Regnet is an application for development, which enable you to have a private blockchain which you have control over.
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Regnet gives you complete control over when new blocks are created which is better/faster for development but may not show exactly how apps will act on the main net when connecting to random peers.
Testnet does not give you as much control over your environment, but this will actually be more realistic for testing purposes.