Okay, that's probably a fair distinction. Don't know enough about anonymous vs pseudonymous to disagree.

I believe the way they deal with this is by having the recipient create a one-time address for every sender, so it is not possible to recognize patterns between senders and recipients. Another thing is that every wallet has two associated keys. There is a "spend key", which is a write-only key that can spend money from the wallet, and a "view key", which can be used to view the contents of the wallet. You can publish the view key if you want that to be public information, but you don't have to.

As I understand it, this happens cryptographically. Send keys can be added to form a larger key, which gets used to sign the pool of transactions. Because the signature used your key as well, the recipient can verify that they have received your coins(from a pool you signed). The important part is that it is impossible to tell who signed what part of the pool, just that one of the people in the pool did. Because all money is pooled together and sent at the same time, it is not possible to read from the amounts sent which transaction belongs to who.

If a state actor wants to deanonymize you...

Then there ain't fucking shit you can do about it. The only thing you can do to keep big brother off your back is to be too small of a fish for them to spend their time on.

Say you buy $50 worth, which isn't anonymous. Then you add to a pool of several thousand or more, which is then sent out to several clean anonymous wallets as smaller fractions of the whole minus some fee. It's not rocket surgery but works effectively well so long as you have good opsec and the pool is trustworthy.

The wallet you sent $50 from is known, but which of the hundreds of wallets that got $10 from the pool belong to you vs others in the pool? They can deduce it from patterns and usage, but it makes it a lot harder. And this is just "newbie's first introduction to anonimized finances"

But unlike cash, the chain exists forever. They can do wild sorts of analysis, which means you need good opsec with clean separation, and lots of obfuscation. But this is nothing new to people in that world.

So yes, it can be anonymous, but it's tricky and may not always be because it has a permanent public record.

.... But if you go thru all that trouble and then just connect to your new shiny dark VPN from your home PC... Uhh.... It's like ordering pizza delivery. Maybe not the best usecase for 'untraceable currency'

You can buy from a physical location if the seller is not a regulated seller (just a random person), chances are they bought the bitcoin from someone else where the coin literally could come from any place in the world. The magic of bitcoin is it is digital so the "coins" can "teleport" around.