Why are there two ways to keyframe-animate geometric transformations? In DaVinci Resolve 14, there seem to be two ways to use keyframe animations with geometric transformations.

One is on the Edit page, using the Inspector. Here it seems to be possible to smoothen out transitions with curves.



Another is on the Color page, with the Sizing tab.



What is the difference between these?  When should I use one or the other?  Is it possible to transfer the adjustments made with one into the other?

I am new to this software (and also video editing). I originally made adjustments on the Color page, but then wasn't able to smoothen the transitions, so I ended up scrapping them and re-doing the same thing on the Edit page.
The video transform tools in the edit page inspector window (zoom, position, etc) actually translate directly to the color page in the "Edit Sizing" window.  In your screenshot your color page is showing the input sizing window, which instructs resolve how to scale the image as part of the input process (very front end of the image processing pipeline).  If you place your mouse over the Input Sizing menu item, you'll see that there is also edit sizing (inspector on edit page), node sizing (associated specifically with the node you have selected in the color page), output sizing (how things get sent to video monitors), and reference sizing (lets you reposition/scale an image when using the wipe function to compare two clips in the color page).