4chan technically does have accounts in the form of '4chan pass', but it's not linked to your posts at all[1] and just removes the ads, and lets you bypass the captcha and some kinds of subnet level posting bans.
There is also the concept of a tripcode, which is basically an HMAC with a key that the server has a user provided code that is shown next to your post. You can use this to prove knowledge of the code. Usage depends a lot on which board you're on, but is generally frowned upon.
Some boards (such as the infamous /pol/) also have IDs on posts (IIRC derived from your IP address and the thread id), so that posts by the same user in the same thread can be correlated.
Other than that, everything is anonymous.
[1] minor exception is the "since4pass" option which just adds a little icon to your post indicating how long you've had your pass. This is basically never used (perhaps because even 4chan posters don't want to advertise that they're paying for 4chan)
There is also the concept of a tripcode, which is basically an HMAC with a key that the server has a user provided code that is shown next to your post. You can use this to prove knowledge of the code. Usage depends a lot on which board you're on, but is generally frowned upon.
Some boards (such as the infamous /pol/) also have IDs on posts (IIRC derived from your IP address and the thread id), so that posts by the same user in the same thread can be correlated.
Other than that, everything is anonymous.
[1] minor exception is the "since4pass" option which just adds a little icon to your post indicating how long you've had your pass. This is basically never used (perhaps because even 4chan posters don't want to advertise that they're paying for 4chan)