I think ma may be the closest thing to Norwegian «modern» in the sense that it is more of a dialect/region difference than an adult/child thing. In my experience, ma is used more in the South and in rural dialects in the US. I’ve heard modern used more in Eastern dialects in Norway. Maybe more curiously, I’ve mostly heard modern used only in the sense of “my mom” (third person) but rarely to address them. Maybe others can chime in on their usage of it. Norwegian has a lot of regional variation.

I’m Norwegian and say «mor» (mother). My mom asked me to use that instead of «mamma» (“mom”) when she thought it sounded childish.

You can also say «modern», but to my ear it’s a little more harsh sounding. Maybe it’s a dialect thing.

In English, I don’t think many adults would normally say “mommy”, but many adult Norwegians say «mamma».

So to me, at least, a closer match is mom=mamma and mother=mor and mommy has no Norwegian equivalent.