The exact number of people in a regiment or battalion doesn't have a fixed rule, it varies from country to country, and even among different types of troops. Even within the same type of troops, situations with large differences in numbers under similar establishments are extremely common.
For artillery units, the most important thing is, of course, the artillery. That's why artillery units are categorized based on the number of cannons. Even the smallest infantry regiment must have over a thousand people; some infantry battalions can even approach a thousand. But an artillery battalion, well, it has far fewer people.
