* The federated approach, where many Twitter like sites can interconnect and exchange messages. One current example of this is Mastodon, older examples are Status.net/Identi.ca
* An indie approach, where everyone basically hosts their own profile and there are no Twitter like sites at all, one instead uses readers that are completely separate from ones hosted profile, just like it was in the blogosphere days. One example of this is https://indieweb.org/
I favor the indie approach as the federated approach seems to in practice often end up with interoperability issues and mono-cultures, at least historically. + there’s still central providers, just a few more than in the case of Twitter, whereas in the indie world everyone is basically a provider themselves and one can eg. put up a static site and use that (through various Micropub tricks and such)