Terminal. Console Vs. TTYS. + Duplicate TTYS windows.

Can anyone explain why when I open up terminal,sometimes it starts with: "Last login: Date/Time on console", sometimes it starts with "Last login: Date/Time on ttys000"?

Also, from my understanding, when a terminal starts with the message "Last login: Date/Time on ttys000", and I proceed to open a second terminal window by going to Shell>New Window, the second terminal window should show "Last login: Date/Time on ttys001", the 3rd terminal window should show "Last login: Date/Time on ttys002" and so forth. Is my understanding of how a new terminal window opens correct? And if so, can someone tell me why sometimes, when i open a second terminal window, it shows the exact same message as the first terminal window (i.e. "Last login: Date/Time on ttys000"), and doesn't start making increasing ttys numbers with each new window until I open a third terminal window (in which it reads "Last login: Date/Time on ttys001)?

In other words, I have three terminal windows open and they read like this:

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Terminal window 1:

"Last login: Date/Time on ttys000"

Terminal window 2:

"Last login: Date/Time on ttys000"

Terminal window 3:

"Last login: Date/Time on ttys001"

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Should I be getting a duplicate ttys000 on my second terminal window? Is that normal?