The only difference, between Tornado Cash and what we have been calling mixers is Tornado Cash is onchain and arguably decentralized. A mixer is centralized.
No that's not necessarily true.
A mixer is just a service that obfuscates the origin of incoming coins. The actual method they go about doing that doesn't matter. Some do a simple CoinJoin. Some buy coins from exchanges and miners with your money and give them to you. Others, like I said above, use smart contracts.
As long as the mixer has access to the private keys for spending the funds then it doesn't matter whether it it is a website or some dApp with a smart contract behind it.
All mixers are privacy tools but not all privacy tools are mixers. (Lightning Network is not a mixer for example. Neither are Silent Payments, nor are Taproot addresses that use Schnorr signatures.)
If you want to go very technical on these definitions, yes you are very much correct. However, these mixers and onchain anonymity platforms, centralized or decentralized, they are all privacy tools created to preserve and protect the anonymity and the privacy of the people who use them. I reckon we can agree on this.
In any case, what is @_act_'s purpose for asking this question?