It is generally recommended that you use Specular to control glossy specular reflections. The specular_roughness parameter of the Standard shader affects the blurryness of the specular reflections. In Arnold, this is called "glossy reflections", or also "specular reflections".
The Standard shader has a secondary layer of reflection, called simply "reflection", which is perfectly sharp and mirror-like. It is only there for perfect mirrors or glass. Not for blurry effects. If you want blurry reflections only you should use Specular. The images below show specular reflections coming from a light source and mirror reflections coming from light reflecting off the surroundings.
The Sky Dome light will also not appear in reflections of the Standard shader. It is recommended to use Specular in combination with the Sky Dome light. If you want reflections to appear then you should use the Sky shader with 'Visible in Reflections' enabled.
Further information about physically based rendering in Arnold can be found here.