How to make Terminal windows persistent
You have "Close windows when quitting an app" checked on the machine that does not restore the terminal windows (your second machine).

This setting is in System Preferences -> General  not in your Terminal preferences.

Uncheck this box to get the desired behavior.  Understand however that this behavior can extend to other applications as well - it is not restricted to Terminal.app

As for the scroll bars, I suspect you will find that the Show Scroll Bars radio button in System Preferences -> General is not set the same on your two machines.