If someone uses a private wallet not on a website , it's very hard to determine who they are and where they are sending or receiving money.
Virtually impossible. And There are things called washing machine services. (Aka tumbler)
Basically you send coins to it. It get mixed with other people's coins. Then the coins are re distributed to a designated wallet.
These services usually charge a small fee.
This makes the money completely untraceable.
You can use the block chain to follow transactions but you can't follow it after it's split up and washed like this.