Both are now only historical in AE as far as I know, though petticoat has been a synonym for slip in some regions and (IIRC) in BE. A true petticoat could be thickish, frilly white cotton, maybe with a lot of lace around the hem, in the days when they were longer and fuller and women and girls might wear more than one at a time, in layers. Historic costumes like Tracht may also have one or more petticoats, that show a little out from under the skirt and are partly decorative.
I picture a petticoat in my mind as worn under a short(ish) skirt, as by 19th-century girls; it would probably be the same word for one worn under a long dress, but those weren't as visible, I guess. The layer that had the wire hoops in it, for a hoop skirt, was a petticoat, I think; in other periods women wore several petticoats for a similar bell-like effect without wires.
When I think of the word underskirt I picture more a skirt that's not really underwear, but just a skirt (in colored fabric, for instance) worn as the not outermost layer. I'm really not up on historical costume, but I picture (vaguely) something like a Victorian riding dress, with a coatlike overskirt in some mud-friendly color that could be lifted or held back to reveal an underskirt in a contrasting, more fashionable color; or an 18th- (?) century dress with panniers, where the overskirt was designed to not meet completely in the middle, showing a contrasting underskirt in a more elegant fabric, like a brocade in contrast to a solid color.
Slips, in contrast, are thin and slippery, made out of fabrics like nylon or other synthetics; a 20th-century phenomenon as far as I know, with their heyday in around the same period as the heyday of nylon stockings.
Not sure if that helps much, since I don't know the exact words for any of those in German, sorry.