Yes, this is Hill of Death, just with the Carentan mini expansion. I have not played World at War, but it is a pretty straight forward war game. Total attack strength versus a defense to create a ratio, roll on a chart, and you are either step reduced or disrupted. You order your troops via operational chits (e.g. Op 1) which tells you the range you can use to order troops. In the above picture, with a range of 1, I could order 2 stacks. Most operational chits are 0, so you can only attack with one hex worth of units. They are drawn randomly from a cup, so you have no idea who is going to attack and with what until the chit is drawn. I really love this mechanic (and lends well to solo play). Units can fire at moving targets but it negates being able to fire later if ordered.
I really like the game. Has the feel of a good, solid war game, but is not overly complex, so it fills that niche between say Command and Colors, and Advanced Squad Leader. Sadly, I don't think it sold well, because people were a bit nostalgic and didn't like seeing a classic revised, so it hasn't had a second print run yet. But I really like it.