It almost certainly means "4% after adjusting for inflation." For example, if spending was cut from $100 million in to $99 million, that was a 1% cut in "nominal" dollars. However, if inflation was 1.03625%, then that $99 million would only buy the same amount as $96 million would have, and thus it as "a 4% cut in real terms."

If the sentence is about economics - "real terms" means adjusted for inflation. In this case you can not replace it by "actually"

i think you are missing context. "In real terms" usually signifies a simpler and restated way to say something. Perhaps they talked about spending cuts in a way that was more defined previously, then stated it again with simpler language.

i think '...with regard to...' is better