Are the 10 inch and 19 inch ring profiles identical?

No. There is a small but useful peculiarity in the 19" ring-only version: the front and lower part of the ring curves outward, making it easier to push an existing cable sideways into the opening.

The 10" ring-only manager does not use that same outward profile.

They perform the same basic horizontal management job, but they are not simply one drawing scaled to two different rack widths.