I really recommend reading this article from Uxplanet: Rounded Buttons or Sharp Angles?
You can bring these points home:
–Sharp squared drawings are generally considered firm / serious / uniformed
–Rounded drawings are considered friendly and harmless.
You can not really identify a pattern from the examples you provided above. Facebook uses sharp corners for connection and rounded corners for recording. Are they friendly on the registration page to encourage you to create an account? Are you already registered and with regard to Login, it is more of a task in company, thus of a square and net design?
Google Previously, their search engine had sharp and squat angles, but now they use rounded corners. Why? Are they unifying their designs to be rounded for consistency purposes, or is it just a look purpose that was chosen by their designers?
I have not seen any research that would require the use of rounded corners for some parts of the application while using sharp angles for the rest. All I can think of is that the rounded models seem more user-friendly and the Sharp models more firm and more uniform. So it makes sense to use them in different places, but what about coherence and unity?
How do we see old models of square cars versus curved rounded models nowadays? Has Google gone from a more boxy design to a curvey design? Better looking, more friendly?