Firstly, the Global.DoWaitFor(...) and Global.DoWaitForProperty(...) actions are both generic and can be used for all kinds of applications - web, desktop or mobile. The Navigator.CheckObjectsExists(...) action is part of the Navigator object and therefore can only be used for web application tests.
In addition, the CheckObjectExists function can use either an XPATH/CSS string or a Rapise learned object name, so it gives you the ability to check an arbitrary XPATH/CSS query without the object needing to be learned beforehand, which can sometimes be useful.
Here are some examples of both syntax options (XPATH vs. CSS):
1) Using an Object ID
You can use the same ObjectID that you would use an SeS(...) command:
2) Using explicit XPATH/CSS
You can use an explicit XPATH expression as well: