Hey, thanks, Thriftymaid! I appreciate your help! :)
Yet, in my head, in some ways it still seems that one can infer that Cathy is running back into the house again in the second example. :) But wait -- 2d example does not say "what" she is running into, as in, specifically, the house - - and "into," by itself, in the second example would make no sense. I'm just typing and thinking out loud here! Ha! Maybe I'm getting it. I had it at one point in my life, I think. I don't know why it's slipped. :)
Thanks, tom jackson! There's some nice detailed information in that link. I'll probably be re-visiting yours and Thriftymaid's answers, perhaps more than once, ha! Thanks, again! :)