Filters and sorts are both included, George. Perspectives can be built to show you either Project or Context mode, with various things hidden from view and the remaining things sorted or grouped in various ways. This lets you build views that show you the things you want to see, and hide the other ones.
A more concrete example would be the "Flagged or Due Soon" view that folks semi-regularly ask about here. It's generally based on context mode, with actions grouped by their due dates, then sorted within those groups by context.
(So everything due today would be one group, and all the items from my "Home" context in that group would be next to each other in that group. The "Due tomorrow" group would do the same thing.)
You can then specify a combination of filters that shows you everything due soon and everything that's flagged, hiding the rest of your actions. An item due today would appear regardless of the flag state, but if I wanted to work on something not due until the year 2020, I could flag it and it would appear in that view as well.
Those are just a few examples - there's a lot of depth here. If you want to learn more, the easiest thing to do would likely be to grab the PDF manual
for the Mac version and read pages 36-39.
As to what controls would appear in the iPad version, there would likely be ones that functioned
equivalently to the controls in the attached screenshot, but I'm not qualified to theorize or speak to how that functionality might appear in the iPad version. Not my area of expertise. :-)