Bitcoin is Bitcoin, a public blokchain, and bitcoins are coins in your wallets with UTXOs waiting to be used by you. How you use your bitcoin UTXOs for transactions, changed addresses, Tor will help you have better privacy and anonymity or have worse ones.
I think What Awaklara is actually on about and which we I agree with is simple, you lose Anonymity and also privacy when you use centralized exchanges that requires KYC to buy or sell your bitcoin because the address from which the coin came into the wallet from or left the wallet into is now attached to your exchange wallet address which already has your identity KYCed to it.
bitcoins basically and technically are fungible so let's say if you buy bitcoins from someone by any way, on CEX, DEX, P2P, you never know that your coins are anonymous or not.
If you buy from decentralized exchanges or any where you have not ever submitted KYC with and you use your Tor or any means to avoid IP tracking, with such address never interacting with any of the KYCed ones, then I can say that you’re anonymous but not with privacy.
But should you use centralized exchanges where you actually have submitted KYC before and you buy bitcoin from there then you’re neither nor anonymous because the exchange actually has this information