Each network's user interface and features differ from one another. For instance, it's relatively easy to find people on Twitter, but it can be quite difficult on Mastodon or Diaspora*. That's because they run on independent servers, also known as pods or instances. Twitter, and most other social networks, run on centralized cloud services.
So, if you want to follow me on Twitter, you can find me with either my uncommon last name or "sjvn," which I've used on every network known to humanity. On Mastodon, though, you'd need my complete address, @firstname.lastname@example.org The same's true on Diaspora*, where you'd find me at email@example.com.
Each network also has its own rules. Some are much more strict than Twitter. Counter.Social, for example, doesn't allow ads, fake news, trolls, or even access if you live in a country known for hosting bots, such as China, Iran, or Russia.
Generally, other social networks are not centered on short, pithy messages. While Counter.Social limits messages to 500 characters. Others will let you write for as long as you like. Hashtags, which can be very useful on Twitter, don't get as much support on any of the other networks.
Another problem with many of them is that they're focused on small communities with a single interest. Twitter enables you to follow different people from many areas. For example, while I care a lot about Linux and open-source software, I also care about science fiction, history, and musical theater. On Twitter, I can follow thought leaders in all those areas. On the other networks? Not so much.
Another difference is that several of these social networks, Diaspora* and Mastodon, run on the Fediverse. The networks are made up of independent servers that are loosely hooked together with the ActivityPub protocol. An excellent way of thinking about these networks is email. No single group runs email. It's a system of common protocols that enables people around the world to connect with each other over different email servers. Some, like Gmail or Outlook, have millions of users, while others have only one user. Regardless, they let you talk to each other. The same is true of the networks on the Fediverse.
That also means each Fediverse site can have its own rules and software. This gives them independence, but it also means they're fragile. If someone wants to close down their Mastodon or Diaspora* instance, your account goes down with them.