Actually is used often as the truth or facts of a situation, for example, in one of your sentences that you used in this post, you write
"In fact I think they are two definitions totally different!"
and you could write
"Actually I think they are two definitions totally different!"
Imagine that you're talking about one book, but you didn't read it, you could say this after you talked about that book:
"But actually I didn't read it".
My knowledge about English is poor, and maybe I could not have explained something perfectly, but I tried to help, I hope that I achieve it.