The common species of pest rodents in New York are house mice, white-footed mice, deer mice, and Norway rats (roof rats are generally not found in NY). Adult mice and rats can be distinguished from each other by their size, some of their features, and fur patterns.
House Mouse
Adult mice are 2.5 to 3.75 inches long (63-95mm), with a tail that ranges from 2.75 to 4 inches in length. Compared to young/juvenile rats, they have large ears and eyes, and a pointier nose. Their body is uniformly colored, meaning that their backs and bellies are roughly the same greyish-brown. The tail is semi-naked and is as long as the body.

White-Footed Mouse and Deer Mouse
These two Peromyscus species with similar appearance and behaviors have two-tone fur with a darker back (grey or tan) and white belly. Because they are the same size as house mice, their coloring is a distinguishing feature.

For rodents other than mice and rats, visit our Wildlife page.
A good resource for rodent identification is the CDC Rodents: Pictorial Key to Some Common United States Genera.