"Ago" is usually used in the simple past tense, indicating something happening in a POINT in time. For example, "the United States became a country 232 years ago". This sentence is in simple past tense, and the event "the United States BECOMING a country" happened at a specific point of the time line, which is "232 years ago".
"Since" is used in perfect tenses, especially the present perfect tense, indicating something happening in a PERIOD of time, which started at some earlier time and still continues at present. The example "the United States has been a country since 1776", uses the present perfect tense to indicate the length of the period of time that the event "the United States BEING a country" has happened, and is still happening.