Not in every country. In the US draft once you’re inducted you can’t choose where they put you
Yes as soon as you're drafted into the military. What Duuring means is that you can object to yourself being called to the military. You can refuse service in the armed forces on ethical grounds.
After that you get two choices: instead of doing 1.5 years of service, or two years of alternative service, like in nursing homes, cleaning, hospitals, garbage services. You can choose what kind of alternative service you'd do yourself. It is either that, or 6 months incarceration.
At least, this was the Dutch system.