The Touch Keyboard (TK) is the large keyboard that automatically appears in tablet mode and can be made to appear in desktop mode.
The On Screen Keyboard (OSK) is a resizable keyboard that can be found under the Ease of Access tools.
In Windows 8.1 the OSK behaved exactly as the original poster wanted. If you used the Dock key on the OSK it would lock itself on the bottom of the screen and other windows would be resized so that nothing was under the OSK. In Win 10 this does not happen.
Unfortunately it seems that Microsoft chose to remove this feature and force both the TK and OSK to float over other windows even when they are "docked".