The process of how the private keys are derived is slightly different. This applies to both the how the (parent) key is generated and then subsequent derivations on this.
In BTC/ETC and most (all other) blockchains, when you enter the mnemonic, it normalized that and then does the pbkdf2 rounds on it. In Substrate, the mnemonic is first taken to entropy before the pbkdf2 rounds are applied. This means that the same mnemonic will yield 2 different private keys in the Sustrate vs other blockchain projects.
On top of this, you have the derivation, which is also different, the HD paths vs the Substrate paths.
Having said all this, there are some wallets (most notably those supporting multi blockchain currencies) that uses their "normal ed25519/secp256k1" keys on a Substrate environment. So one you have a key and can sign, it doesn't matter. The difference is rather how you get to the key.
As a note, when connecting to an ETH-compatible chain, e.g Moonbeam, the apps UI does give an option to use ETH-standard mnemonic -> seed as well as the ETH standard derivation paths.