For your secondary question, you can see Cass didn't realize it's a TARDIS until the Doctor mentioned it's bigger on the inside - a telltale sign you're dealing with Time Lord technology. That's what tipped her off.
As for your main question, Cass's reaction makes it quite clear that at that point in the war, both sides had committed such atrocities that any moral distinction was quite blurry, especially from the outside. By the end of the Time War, Rassilon, leader of the Time Lords, was willing to destroy time itself and all the universe to ensure the Time Lords' survival.
The old series, where the Time Lords were still occasionally encountered, made it clear that they're not particularly nice people, on the whole. Many of them are ruthless, amoral or downright vicious, and their dictum forbidding interfering with other species and their timeline was there mostly to protect those species from Time Lord meddling, not necessarily from some Prime Directive-like imperative to let time take its natural course.