What are the differences between “at war with” and “at war against”

Question

Can both "at war with" and "at war against" mean the same thing. In my opinion, both can mean the same thing, but can also mean the opposite, would you agree with this, and why?

For example:

They are at war with everyone at all time and wonder why everyone hates them.

Answer 1

No

You could say either of the following:

They are at war with everyone ... (at war is a prepositional phrase)

The war against everyone ... (war is a transitive verb)

but not:

They are at war against ... (this is two prepositional phrases attempting to merge into one)