Difference between "Carry on" and "Carry on with"

Question

Is there a difference in meaning between the two? For example:

1. Carry on the mission
2. Carry on with the mission

Answer 1

It really depends on the context, meaning, and message you are trying to convey.

"Carry on" IS the action.

I cannot believe the child would carry on like that in public.

"Carry on" on its own is a general command and is the same as "carry on with..."--one has less information and one has more.