In my experience, both terms are used to set off an unexpected truth:
"One might think my dog Puffball is a gentle pet, but in fact she has two rows of razor-sharp teeth and randomly attacks guests."
Or to emphasize further detail:
"Puffball is a longhaired Pilchet. Pilchets were originally bred to hunt mice under the beds of slatternly housewives, where they were able to successfully camouflage themselves among the dustballs. Pilchets were very aggressive hunters; in fact, a full-grown Pilchet could easily dispatch a dozen mice a night. To some this might seem cruel, but the Pilchet could actually kill a mouse far more quickly and humanely than poison or a trap. And since the Pilchets eat their prey, there were no dead bodies to dispose of."
However, "actually" is commonly used to express surprise, rather than "in fact."
"I can't believe you actually bought one of those horrible Pilchets!"
- For Teachers