The Doctor-Donna has all the knowledge of a Time Lord ...
Maybe it's "obvious", to someone with Time Lord experience, that the Fourteenth Doctor isn't the same regeneration as the Tenth Doctor. Heck, it's even clear to us as viewers: I'm not sure how much of "David Tennant looking older" we're meant to just ignore (he'd already filled out a bit when he came back for the 50th anniversary special, and in that case he was meant to be the same regeneration as the Tenth), but he also acts slightly differently, as if he's been through a lot since "Journey's End" (which he has). Perhaps she can look into his eyes and see how much older they are, more of a difference than would fit within a single regeneration.
... as well as the instincts of a human woman.
On the other hand, the Eleventh Doctor at the end of "The Time of the Doctor" both looked and was a hell of a lot older than at the start of the same episode, after spending centuries defending Christmas. So it's possible for a Time Lord to age significantly within the same regeneration. How did Donna know that the Fourteenth Doctor wasn't just a significantly older Tenth?
Lest the following sound like mere headcanon, here's a quote from the Doctor-Donna in "Journey's End" (emphasis mine):
META-CRISIS DOCTOR: But that's brilliant!
TENTH DOCTOR: Why did we never think of that?
DOCTOR-DONNA: Because you two were just Time Lords, you dumbos! Lacking that little bit of human - that gut instinct that comes hand in hand with Planet Earth. I could think of ideas you two wouldn't dream of in a million years. Whole universe has been waiting for me!
She's explicitly said that what differentiates her from the Doctor(s) is gut instinct, and that would certainly be a reasonable explanation for how she immediately knew that the Doctor she saw in "The Star Beast" was a different regeneration from the one she'd travelled with before.