I know how to get one window on the mac and a different window on the second monitor. I don't how to get a full screen window on the second screen though. Because you have to untick mirror displays to do that and I can't access system preferences when the window I want to go on the second screen is full screen. Does that make sense to you? Is there a way round this? Thanks.
It kind of depends a little on which version of the Mac OS you are running. Based upon the link
you posted in another thread, you appear to be running a Mid 2015 15" Retina MacBook Pro with discrete graphics. A Mid 2015 model rMBP (Retina MacBook Pro) would have at a minimum 10.10.3 or higher. And 10.10.x (aka Yosemite) and 10.11.x (aka El Capitan) will both work pretty much the same way for this scenario.
There are multiple "features" at play here...1) multiple monitors; 2) full screen mode; and 3) Mission Control/virtual desktops.
So, it seems you know the basics of multiple monitors, but just to be on the safe side I will go over it again. As it seems you know, with multiple monitors, you can operate with in either mirrored mode (same thing on both screens) or "extended desktop" mode (have each desktop act as if they are "expanding" your desktop/screen). When you open System Preferences and then click on Displays, you should get a System Preferences window on each display (i.e. in your case, if running a single external display with your rMBP, then one window on the rMBP's screen and one on the external monitor). The "primary" screen will have the "primary" System Preferences window (i.e. it will maintain forward and back arrows, "main screen" button, and a search field as well as three tabs when in the Display settings...the tabs will be Display, Arrangement, and Color), while the "secondary" screen will have a "secondary" System Preferences window that will appear on that "secondary" screen when you go to the Display preferences, but will disappear when you go back to the main System Preference screen (this "secondary" window will only have Display and Color tabs and will not have the forward/back arrows, the "main screen" button, or a search field). The reason for this is to allow for different resolution & brightness adjustments (Display tab) and color profile (Color tab) for each display. The Arrangement tab is more about affecting ALL the displays rather than just a single display. And the Arrangement tab will have show a "representation" of the two displays as well as have the Mirror Displays checkbox that you mentioned. I mentioned "primary" and "secondary" displays. You pick that on the Arrangement tab. The represented display that show a white bar across the top represents the "primary" display. While menus will actually appear on either display when that display is "active" (i.e. you are actively working in a window on that display) in newer versions of the Mac OS, this was not always the case. It used to be that the menus would only display on one screen...the primary screen. You can change which display is primary by dragging that white bar to another display in the Arrangement tab. And you can rearrange where you want the two display to be relative to each other by dragging the representation of the display to where you want it. You may or may not have know most of that.
For fullscreen mode, as I mentioned in the other thread, you basically go into and out of that mode either by the keystroke combo I mentioned or by using the green button in the upper left corner of a window. When you go to full screen mode, the menus will be hidden. They will appears when you move the mouse up to the top of the screen. Or you can do the Control+F2 keystroke when in full screen mode to make the menus appear. And when you go into full screen mode, that full screened window becomes another virtual desktop. Again, you may or may not have know some/most of this.
And that leads us to virtual desktops and Mission Control. With newer versions of the Mac OS, each display will have their own set of virtual desktops. The Mac OS has for a while "aligned" the virtual screens in a horizontal alignment. You can switch between virtual desktops by swiping left or right with three fingers on your track pad; or by pressing Control+left arrow (to move the virtual screen to the left) or Control+right arrow (to move to the virtual screen to the right). Or you can switch virtual screens by entering into Mission Control by either pressing the F9 (this is the default, but it can be changed) or clicking the Mission Control icon in the Dock (a black icon with what appears to be orange, blue and green boxes). When in Mission Control, you will see all your virtual desktops for each display arranged along the top of each display. You can then click on any of those virtual desktops to make them active. Along the bottom of Mission Control will be a representation of each application and windows for that application that is open on current virtual desktop of each of your displays. You can then click on an application or specific window of an application to go to that application or window. You can add new virtual desktop to either display by moving your mouse cursor to the upper right corner of the display you want to add another virtual display to...when you do, a plus sign will appear...if you click on that plus sign, then a new virtual desktop will be created.
Now, with that long winded explanation out of the way, I can try to answer you question.
I am not quite sure I understand what you are asking to do. It appears that you want to have an second application go into full screen mode on the second display. If so, you should have just the Finder displayed on the second screen when you go into "extended desktop" mode (see above). This Finder display will the only virtual desktop on that second display (i.e. if you go into Mission Control, only one virtual desktop should appear across the top of the second display). To then get a full screen display on that second display, there are two basic ways to do this.
1) The traditional way. On the main display, you will need to NOT be in full screen mode (i.e. see multiple windows and menus across the top). Then click and drag the window of the application you want to put into full screen mode from the primary display to the secondary display. Once the window you want to put into full screen mode is on the second display, then click the little green button in the upper left of the window to put that window into full screen mode on the second display.
2) Use Mission Control. Put the window/application you want in full screen mode on the primary screen. Then enter Mission Control. Find the virtual desktop of the full screen window/application that you want on the second display along the top of the primary screen. Then click and drag that virtual desktop from the primary screen to the secondary screen.
Does that answer your question?