During our time on Srb2 we are so used to calling levels like GFZ or THZ 'Coop' levels. In reality these levels are indeed Coop since we play them with more than just one player, especially in Multiplayer, however these levels do not deserve the name.
There is in fact a difference between Coop and Single Player. Other than the most obvious reason, which is Coop is for more than one player and SP is for only one, there is another difference.
Single Player levels, like the name describes, are levels with an exit that a single character can finish. Common examples of this are levels such as...well all of the SP levels in Srb2. Most of these levels have multiple ways to the exit that different characters can take and can finish without the help of other characters. This is what distinguishes SP from Coop.
Coop or Cooperation is a type of level that requires the skills of different characters to finish a level. Unlike SP, Cooperation levels can not be finished with a single character. Such levels require different characters and their skills to finish the level.
Here is simple situation of such a level. There are 3 people on a server playing a Coop level. There is a Sonic, Tails, and Knuckles player. As the players proceed they get to a ledge with a death pit beyond. The Knuckles player can just glide beyond and get to the other side. However, the Sonic player can not go on since the players' thok won't take him the distance necessary to get to the other side. Therefore, the Sonic player needs the Tails player to fly him over to make it to the other side. As they continue, they encounter a maze with death pits all over the ground. To their right there is a door that can only be opened by a switch. Neither the Sonic or Tails players can get to the switch which is located beyond the maze. The Knuckles player must use their gliding ability to get through the maze and to the switch for them to continue. The level goes on with situations like and unlike these throughout the whole level.
If you have different thoughts on this or are just looking to argue for no particular reason feel free to post them here.