Round corner guards are normally called "Bullnose" corner guards and they are typically used when the corner of the wall is rounded (is a bullnose corner).
Do I Need Round Corner Guards or Can I Get 90°
You should always get the corner guard that matches the radius of the wall corner for three reasons.
First, aesthetics. The designer of the building designed rounded corners as part of the aesthetic of the whole interior and will want that aesthetic to remain.
Second, superior damage protection. When a corner guard matches the shape of a corner, any impact will be distributed across the whole corner guard because it is both rigid and flat against the wall corner.
If you put a square corner guard on a rounded corner, damage will be focused on screws/nails and not distributed throughout the whole corner guard. That is, there is a concentration of force in one spot as opposed to distributed and thus weaker and harmless.
Third, installation. If you have a rounded wall corner and install a square corner guard, it is easy to get a corner guard that is too small for your corner. This is because a rounded corner has a corner bead that is larger, due to the round radius, and thus the area where you should screw into is farther out on the corner bead. If you get a corner guard that is too small you will screw into the corner bead itself and the screw will go through the void between the rounded corner and the corner guard.