There's survival, creative and hardcore, but I've never heard of adventure mode before. I tried it out and to me it was the same thing as survival… Unless I didn't try much. What is the difference with adventure mode and other modes?
Adventure mode in Minecraft?
 Eddy  
 Adventure mode only let's you break glass, It was made for custom maps.
pedro 
 The main difference to survival mode is that you can't break most blocks without the correct tool.
Example:
A shovel is required to break sand or dirt
 An axe is required to break wooden blocks… And so on.
Matthew