"I am calling an ambulance."
Translation:Dzwonię po karetkę.
They're not. I'd say that you use "po" when you want someone to arrive, so even if it's your mom, you can either use "do" for just calling her and "po" when you want her to come.
A potentially bigger problem is when to use "do" and when to use "na". Mostly it's "do", but then you call "na policję" (calling the police), "na pogotowie" (emergency services, by default you usually mean the medical ones, but it can be different), and you'd probably find some other ones. Or you can call "po policję" to make them arrive as well.