As in, traced back to the same user. Assuming you only had the BTC addresses and no other information.
If you want any privacy in bitcoin, you should use a wallet that offers "Coin Control" features, such as Bitcoin Core, and control your inputs and your outputs. There's no other way. If you don't, multiple addresses on the same wallet will in fact be linked and maybe you don't want that.
Segwit and lightning network to enable confidential transaction, coinjoin etc is the only way to improve privacy.