Ethereum network - wallets or addresses tracked?

Perhaps a stupid question but as far as I can tell, on the bitcoin network/btcscan it feels fairly clear that if a total value of assets is given its for the addresses. That is to say it can only show what has been received from and sent by that address and give the difference. On etherscan it admittedly shows 'Address xyz,' not wallet xyz but ... well I suppose I always assumed that it showed the wallet's total token holdings - that is to say what the user sees in their account. I suppose this assumption is built on the fact that the standard convenient browser based ERC-20 wallets don't tend to change their addresses whilst deterministic wallet holders change their addresses frequently.

TL;DR - Does the ethereum network track wallets or addresses (See actual post for articulation)?

(Reposted because I forgot to add a flair then found out I can't... doi)