Both surfaces are real tennis. However, I agree with Nick for the most part. Any great athlete can pick up a tennis racquet, learn to hit a forehand, and be a solid play court player. If you only have a great forehand, you can be good on clay. If you only have a great serve, you can be good on grass. But the forehand is a much simpler stroke, and nearly everybody develops a solid forehand before a solid serve. The forehand is a very natural motion for somebody who is athletic. They won't have the beauty of a Federer forehand, but they can muscle through it like a Nadal forehand. Nadal doesn't have great forehand technique, but it works fantastically. The serve is much harder to do well without proper technique. Many athletes try out tennis, and they get the forehand comfortable in one session, but it might take weeks for them to develop a decent serve.
If you don't have that one dominant shot (serve for grass, forehand for clay), you can get by on clay purely with your generic athleticism (assuming basic tennis skills are there); running back and forth, just hitting decent shots back. But on grass, that doesn't work because the court is faster. You need more tennis-specific skills, but you don't need as much generic athleticism. You can get by with basic athleticism, but great tennis skills; variety in forehands and backhands, slices, short and deep, approach shots, half volleys, volleys, etc.
I'm not saying one surface is better than the other, they're just different. Clay promotes generic athleticism over tennis-specific skills. Grass promotes tennis-specific skills over generic athleticism. Obviously both skill types are required for both surfaces, they just each lean towards a different type a little more. Personally, I love when I'm coaching on clay, or just playing for fun, but if I'm competing, I'd much rather be on a hard court because it suits my game more. I've never played on grass personally, although it is on my bucket list. I prefer watching grass because of the variety of points and play styles, and I love watching great servers as well, whereas I don't enjoy watching somebody stand back at the baseline just getting balls back all day as much; although I do enjoy watching the likes of Wawrinka, especially when he won the French Open, but he crushes the ball rather than relying on running around to get to every ball and putting it back in play.