"as-rolled" tells you about the material properties. Generally "as-rolled" means that the material has not been heat treated after it was formed by rolling.
"Coil" tells you about the form of the material when it is shipped from the steel mill.
Coil does not have to mean how it is shipped. Coiled produced plate or strip can be flatened and cut to size and shipped. The coiling temperature in addition to the final hot rolling temperature can dramatically affect mechanical properties. Coiled skelp is also used to make welded pipe.
