I notice some posts on my Facebook Timeline have options for "Show on Timeline" and "Allow on Timeline" but I couldn't find what is the difference between them.
The post that has these options was posted from the Run Keeper app. It might be only for app generated post, but I'm not sure.
Best Answer
Show on Timeline
forces the Activity to be shown on the timelineAllow on Timeline
just enables posting of that activity to timeline, it still may or may not end up on your timeline...the power to whether show or not resides with Facebook's feed algorithmsyou can always watch over
https://facebook.com/{your username}/allactivity
to toggle show/allow and also look over what the information apps are logging onto facebook