Is there order in each discipline, activist atheism or militant atheism? Or are these expanded terms to qualify an atheist order? Seems to me atheism will always be without order.

I would say yes but general society would say no. I think activist would include simply being upfront about not-believing and being unafraid to stump for the right to not be subjected to religion. Militant is a more extreme form of protestation.

Maybe "tone?" Activist atheism is important. Perhaps militant atheism is just a disparaging label when someone thinks an atheist is being mean. So much subjectivity in volved, here, but I guess the difference would be the sophistication of one's diplomacy efforts.