Focus and Activation are closely related.
Focused window - this is the window that receives keyboard input. The focused window is always or is always contained by the Active window.
Active window - this is the window that is rendered as key - i.e. the one that contains the focused element. Different platforms will render this differently and may show additional affordances e.g. a different treatment in the window switcher.
A "top level" window is a window that has no parent other than window manager constructs. Think of a Chrome window.
An "activatable" window is a top level window that can be activated. Not all top level windows can be activated at any given time. For instance in Ash, if the screen is locked calling GetActivatableWindow() for a window behind the lock screen may return a window in front of the lock screen, whereas GetTopLevelWindow() will return the non-activatable toplevel behind the lock screen. For this reason GetActivatableWindow is a method most useful to the focus/activation implementation, and GetTopLevelWindow is the method most useful to general application code.
In Aura, the CoreWM library provided by Views handles focus and activation changes in the class FocusController. The FocusController implements two interfaces - aura::client::FocusClient and aura::client::ActivationClient. Every RootWindow must have an associated Focus/ActivationClient implementation associated with it, though several RootWindows can share the same implementation. For Desktop-Aura, each top level DesktopNativeWidgetAura creates a separate FocusController for the associated RootWindow. For Ash, there is a single FocusController shared by all RootWindows managed by the DisplayController.
The FocusController tracks the current active and focused windows, and sends notifications when either of these change to registered implementations of aura::client::FocusChangeObserver and aura::client::ActivationChangeObserver.
Views also tracks focus, for views::View subclasses within a views::Widget. Think of it this way. In the Aura world, an aura::Window can have focus, and can have an embedded View hierarchy via NativeWidgetAura/Widget. Within that focused aura::Window there can be an individual View that has focus, e.g. the omnibox textfield vs. a button etc. Each toplevel views::Widget has a views::FocusManager which handles View focus. It also handles things like focus traversal. Focus traversal is what happens when you press Tab. The traversal code figures out what View to focus next when you press Tab or Shift+Tab.
When a views::Widget is deactivated, its FocusManager stores the focused view in ViewStorage for restoration later. The history behind this is somewhat vestigial but the storage/restoration step is still necessary. When the Widget is later reactivated, the last focused view is refocused. This is true in both non-Aura Win32 Views and in Aura Views.
As far as what can be focused or activated in Aura, FocusController delegates to an implementation of the FocusRules interface to determine what can be focused or activated. There are different implementations for Ash (AshFocusRules) and Desktop-Aura (DesktopFocusRules). These rules enforce specifics like not activating windows behind the lock screen, etc.