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I wonder if there is any difference between "1" and "2".
1. The kids are acting up again.
2. The kids have been acting again.
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"Acting up" and "acting out" are fixed expressions - possibly idioms. They refer to forms of misbehavior.

"The children are acting," in the generic sense could mean they are performing in a play; or "play acting," as in "pretending to be X."

"Pretending to be X" could be "for fun," or it could be for some devious purpose: pretending to be sick, pretending to have been kicked out of school.
It would be different from a simple lie in that the "actor" affects the false emotional state.

Quit acting! There's nothing wrong with you!
Comments  
1. The kids are acting up again. -- Fine; "acting up" = misbehaving.

2. The kids have been acting again. -- Correct English, but has a different meaning, referring to their participation in a stage performance, or something of that nature. (At least, I am not familiar with the use of "acting" to mean anything like "acting up".)