I hope I can clarify a few things here.
The Properties WINDOW is a dockable window that allows you to view and edit the properties of the selected modeling object - element, connector, diagram, attribute or operation. You are most likely to open the window at the start of a work session and leave it there as you work across your model. Whatever object you click on, the window immediately shows its properties.
The Properties DIALOG is a free-floating dialog box that helps you to view and edit a smaller range of object characteristics but a wider range of features, in that you can edit Notes, Requirements, Constraints, Scenarios, Tagged Values, Attributes etc. from within the dialog (these are not in the Properties WINDOW but have their own WINDOWS). The Properties dialog is specific to the selected object - you select the object, open the dialog for that object, do your work in it and then close it; you cannot move on to another object while the dialog is open.
Talking about elements (I have not gone over all the other object types yet) the options could be more consistent, but while one Properties option might just be 'Properties', there should always be another that states whether it is for the WINDOW or for the DIALOG.
Now, 'Special Action' - a number of element types have special characteristics or behaviours. For those elements, the 'Special Action' option opens a different dialog to define those special characteristics or behaviours. If the element is not a special case, then the option opens the Properties DIALOG. It basically means 'this option opens a dialog that is specific/special to the element you have chosen' whilst the associated 'Properties' option means 'this option opens a window that can show the properties of any object'.
HTH