Distinction without a difference - In the USA the controllers will respond to "Declaring an Emergency" and "Mayday", they know both words. The issue in many different incidents was the pilots did neither one. This crash was actually kind of a DC-3 style crash, you can see losing an engine on a heavy DC-3 right after takeoff and then the 80 year-old good engine going bad when flogged to max power to keep the plane in the air, but I would guess the assumption from ATC on a 737 is the plane had plenty of power on one and they were going to get things cleaned up and organized because the plane could do it no problem.