To determine the exact model - - -
Does the pistol have (1)a button type magazine catch, or (2)a heel clip type?
Does it have (1)an exposed hammer, or (2) a smooth-backed slide, concealing the hammer?
If the answers are both (1) you have the more modern type Colt .380, a "Government Model" (NOT to be confused with the 1911 service pistols,) a Mustang, or a Pocket Lite, depending on barrel length, magazine capacity, and frame material.
If the answers are both (2) you have the classic Colt Pocket Model, what is currently called the Model 1908. It was discontinued after some production during World War II.
Both types are desirable, with a nickled 1908 being rather more valuable.
Best,
Johnny