PhotoStream on iPhoto-MacBook is different from PhotoStream-iPad
Apple has a fairly comprehensive troubleshooting article for isolating any inconsistencies like you have observed and clearly, the design of Photo Stream is that there is one set of pictures available from the cloud (the web  interface) as well as each device that has the stream enabled.


TS3989 - iCloud: Photo Stream troubleshooting


Why not work your way through that document and then ask a second question if needed if you run into problems on a specific step? I like to power off both the devices and then start with one to work through the process to see if it's working properly, and then proceed to the next device or computer.