There's quite a bit of variation of "chinese kickboxing" out there, mostly because of the history of modern chinese sport fighting:

-In general, "Kung Fu" sytles have traditionally been "chinese boxing schools." Traditional sparing for most kung fu styles is to go out back and beat the crap out of each other bare handed. (Not as bloody as you might think, punches to the head are less common when you're hand's aren't wrapped - palm strikes don't do the same damage to the skin on the face as bare knuckles.)

-When I trained for "chinese rules kickboxing" in the mid 90's, we were competing with US Muay Thai rules.

-Since then, "San Shou" has formalized in the US, and I've seen two different types of "San Shou"
A)The type competed in the Tiger Balm in Vancuver, which is essetially kickboxing with a limited variation of techniques (punches to the head are allowed, but only a certain number consecutively, kicks to the legs are allowed, but not to the inside of the thigh, etc.) With that there are also various throws that are allowed, and ground fighting is not seriously entertained. (The last time I looked at these rules was 2002, so it may have changed.) Generally this affair takes place on a mat and opponents where shinpads, gloves and head gear.
B)Another type of "San Shou" i've heard of taking place takes place a similar type of mat/ring, but is much more like MMA, with most stand up techniques allowed, and limited ground fighting tolerated, with some bouts won with submission holds. (I have not actually seen this in person.)