Consider these two sites: Area 51 and Area 51 Discussion Zone.
The latter site is considered to be a child of the former, and you have a single shared account between the two of them. Each site, though, has its own page for your account; that page shows the shared rep (from the main account), but the badges and activity on each differ.
This works similarly to the way accounts work elsewhere across SE. For instance, you have an Apple.SE account, which is then shared with Meta.Apple.SE. Note again that that's one account (same rep, for instance), but two separate pages with separate history.
Now, as far as "related accounts" go, your Area 51 and Area 51 discussion accounts aren't related to each other as such, because they're one single account. You can see your related accounts on your network profile page. When you clicked "Copy profile to related accounts," you copied your information from your Area 51 account to your Apple, SO, Web Apps, SU and UX accounts.
If this isn't completely clear, let me know what you're still having trouble with.